Firstly, the earthquake had no effect on the Washington Naval Treaty which had been negotiated almost two years earlier. The building of the battlecruiser Atago had been stopped by the treaty and she was thus left at Yokosuka and wrecked by the earthquake. Without the treaty, she would have already been launched. It had been planned to convert her like her sister ship Akagi into an aircraft carrier. After the earthquake, the slower Kaga was converted instead.
Secondly, can I repeat an earlier posting from
https://www.alternatehistory.com/discussion/showthread.php?p=2780959#post2780959
At the start of 1923, the Japanese economy appeared to be in fairly good shape and no one doubted that the large loans taken out to pay for the Russo-Japanese War of 1904-5 could be repaid on time and in full. Prospects had recently been improved by the Washington Naval Treaty of 1922, allowing a reduction in both taxation and government spending. In retrospect, there were some dangers as unlimited demand and lack of competition during WW1 had created a bubble as well as very rapid growth.
However, on 1st September 1923 there occurred the Great Kantō Earthquake which devastated the region around Tokyo. Suddenly, the economic outlook was transformed. New loans had to be negotiated at short notice from America at high cost. The earthquake became linked to the bursting of the WW1 bubble because the Bank of Japan extended special emergency loans to banks in the affected Kantō Region. Naturally banks brought all their pre-existing bad debts to the BoJ! To pay for all of this and due to reduced tax revenue, government spending had to be reduced, notably by reducing the size of the Army. As the BoJ eventually stopped supporting every bank with bad debts, the banking crisis had been only been postponed and occurred in 1927.
Now, Taisho democracy could be considered fully established from June 1924 when the government led by Kiyoura Keigo fell after defeat in an election and the new government extended the vote to all male citizens over the age of 25 in 1925. Kiyoura had had the support of the Genro and the bureaucrats but was defeated by the political parties of the Diet. This timing meant that Taisho democracy had to start by coping with the consequences of the earthquake. The less obvious consequences included attacks by the Seiyukai party on the governing Minseito for paying too much for the American loans, attacks on all politicians for having the BoJ pay out to their friends and the IJA beginning to organize a political movement to defend itself against further cuts.
Thus Taisho democracy would certainly have had a better chance of survival without the Great Kantō Earthquake.
