Why would it be so expensive diplomatically really? The French don't care if the British lose Cyprus and the British could accept if they keep their bases there, especially if there is civil unrest on the island. Also Cyprus isn't just a patch of land. It's part of the homeland being occupied with living Greek majority inside. Greece can demand more than one thing and what
Sphenodon meant that this matter would be solved before Suez Crisis could well be after the Indian decolonization.
I'm sure the British would be super thrilled to entertain the Greek demands for Cyprus right after losing the entire British Raj... While the wound is still fresh... For no other reason but just because Greece wants Cyprus... They'll be super thoughtful... The French too... it's not like they'd fear a colonial "domino", that by setting free one colony, they embolden all the others to demand and press for their own independence...
So you clearly jumped with with conclusion as I see it. You can have first the WW2 peace and then after 4-5 years with the creation of UN and NATO as well as the abandonment of India by the British a new treaty specifically on Cyprus.
This is incorrect assessment IMHO. For the obvious thing I have mentioned multiple times: USSR. Greece would be on the border with the Black sea straits and would always need to have a working and ready army, navy and airforce.
ITTL if the rest of the Balkan states join NATO, then the Bosporus Straits alone, a coastline of just Eastern Thrace (or even possibly Bithynia too), it is about the size of the Romanian coastline in Dobruja. A nothingburger... not nearly enough to warrant anything more than local defensive preparations and a sizable unit presence locally. How does that help the state of the Hellenic military as a whole moving forward is beyond me. After all, the Ottomans had half the Black Sea (or whole if you go further into the past) on top of the Bosporus Straits, the Russian boogeyman was always there and that didn't stop the Ottoman military from severely decaying over the years...
Also the junior officers of WW2 will be active till the 60's providing said experience.
So what happens after the 60s?
Now if you want more battle hardness which to me is warmongering to be real you can help America in whatever shit they go in like Korea, Vietnam, Israel wars and all the African civil wars if you want.
That's the whole point, US led interventions are a really bad cause to bleed and die for, because you end up gaining nothing from the whole affair, as US doesn't really reward its allies, the US are firmly in favor of uber rigid borders. The European powers on the other hand... Suez Crisis is the defining event that can alter the balance of power within NATO one way or another... I'm not saying that the US should not be the prime nation in NATO, I'm merely saying that the US could become more akin to a first among equals in the ITTL version of NATO, instead of overly dominating the military alliance like IOTL, with the European powers retaining a bit more of their powers, for a more fair, balanced and interesting "free world".
I don't know why you compare Greece with France OTL though. France had the economy to support all of that activity Greece not so much... for now to be honest. Still joint exercises with NATO would be enough for a good level of battle readiness.
ITTL Greece is more than likely the most powerful nation on it's region, that of the Balkans & the Middle East. ITTL Greece is much much more powerful than IOTL Greece, and it would be a shame not to take the slightest advantage of that. While it is true that ITTL Greece still is considerably weaker than France, that doesn't mean that Greece cannot take more initiatives than IOTL, simply because it didn't take any such initiatives IOTL, for ITTL Greece has a completely different political/economical and even social situation, that any such reasoning is flawed beyond reason. Similarly, Greece could possibly work with France in Northwest Africa, to ensure the stability of the region, but that's later down the line.
Greece needs to develop itself far more to be compared with France and its geography makes that said development more expensive. I don't say to ignore the military but going on pointless foreign adventures is not the best way to spend money.
If ITTL Greece were to enhance it's cooperation with France, such as participating in French led interventions aiming to stabilize West Africa in the future, thereby becoming a strategic partner to France, then funds from French industries or even French public funds may flow in to Greece both as reward for the assistance offered, as well as an effort to strengthen ITTL Greece's military and even economic capabilities, to be more useful as a strategic partner in the future for France. After all, IOTL France did prop up Poland's industry, infrastructure and economy in the interbellum period. And that with the weak government system of the Third French Republic. Now imagine what France could do for Greece ITTL under the powerful presidential system of the Fifth Republic.
Having an Alexandrian Free State is a clear money sink just take all the refugees at once, it would be preferable to both you and Egypt(if they expel them).
Egypt would never expel the Copts on it's own, there isn't any reasoning for that unless Greece participates in the Suez intervention and enlists them in a substantial manner. The Greek people residing within Egypt are going to be deported no matter what, only this time, if Greece stays out of the whole affair, they might immigrate to Greece in larger numbers than IOTL, instead of the United States, taking into consideration ITTL Greece's better economy, better demographics, more available (arable) land, more work opportunities and a bit less urbanized centers, but 4-5 major ones, (Athens, Thessaloniki, Smyrna, Constantinople, Patra or Prusa? post war), all that makes immigration to Greece all that more attractive, considering that the deported Greeks immigrated to the US in search of economic opportunities, that ITTL they might just find closer to home. The main issue is that the deported Greeks from Egypt are just a mere 500.000 people, not nearly enough to settle and secure the Anatolian lands gained post war (if that includes Biga, Bithynia and all of Caria, other than Constantinople.
That would leave these aforementioned lands sparsely populated, which would increase the threat posed to them by neighboring Turkey, to seek to reclaim them in the future. Maybe not in a decade, but in 2 or 3 decades they could start a war over these regions, if they aren't secure enough, considering the advantage that higher birthrates would provide to Turkey in the future, in the event of any future war. ITTL Greece participating in foreign endeavors would in turn make both Turkey's populace and political elite be extra weary of Greece, similar to how Western Germany didn't even considered contesting any disagreements with France militarily post WWII, for any reason, even for Saarland.
The "Free City of Alexandria" state would be pretty much doomed to fail, as soon as Israel loses control of the Sinai peninsula, but again, that is not necessarily a bad thing, for it would provide Greece with a lot of Coptic refugees (maybe even a few arab muslim allies that fought for Greece, similar to the Circassian allies that were granted Greek citizenship ITTL, or even the example of the Harki in Algeria IOTL), that would in turn help secure Anatolia for good.
So long story short, the best foreign policy is an assertive one.
Going to Lebanon is just out of nowhere and getting mixed in a seriously complicated situation.
You've completely lost the point with Lebanon here, never said that Greece should colonize it, idk why you even assumed as such, simply said that Greece could pressure France to change their Lebanese protectorate borders, for additional stability in the region, and to further their influence over the state, by influence I clearly mean soft power/popularity, not boots on the ground or anything like that you've just assumed here, because I clearly have a "warmongering" vision for Greece, everything I advocate for must be warmongering stuff welp...
Building the EU and having a prominent place there is Greece's best bet on the future not going full Alexander the Great on its neighbors.
Debatable, ITTL Greece could even create a Balkan group (think of Visegrad Group or the informal northern EU states group led by Germany, but instead putting forward whatever Greece's interests are), with within the EU to defend its interests, if the Balkans remain outside of the Warsaw Pact post WWII. But that is after economically dominating the Balkans. Regardless, the vision of an ITTL Greece with more assertive foreign policy isn't remotely incompatible with EU ideals, no more than France's IOTL assertive foreign policy is.
On this note I wonder will there be Greek oil on the plans in the future? I mean OTL there is the whole EEZ thing with Turkey and the whole thing is pushed back but ITTL all the potential oil deposits would be on Greek EEZ and on top of that Greece would be able to enforce it. Just throwing it out there.
Yet another reason why participating in the Suez intervention would be good for Greece ITTL. The Egyptian oil/gas fields in the Mediterranean sea e.g. Zohr field for example. Not that the Aegean doesn't have it's very own oil/gas fields, but it's much easier for the author to accurately calculate the yield of a operating oil or gas field with all fossil fuel reserves in the area already discovered accounted for, having been made public knowledge at this point, than either speculate on the actual amount of oil/gas reserves, because not even that is known for the Aegean basin, due to the disagreements between Turkey and Greece IOTL, much less calculate a realistic amount of production for the entire Aegean basin.
Otherwise, in order to be plausible, ITTL Greece would be stuck with just the really conservative estimate that the author would have to go for just the Aegean basin reserves, so that won't account for a whole lot, it would be quite lucrative for Greece yes, but not nearly as much as it actually should be.