The interwar bakufu came about because the parliamentary system (like pretty much everything in Meiji Restoration Japan) was based on trying to mirror the German system only with modifications to avoid its known failure modes. One issue was that the Prussian civil service and military tended to capture the electoral system for their own purposes, and so government employees, which included the military, civil servants, teachers, and even postmen were barred from voting.

They didn’t like this so they went about trying to find non-electoral means of capturing the government. There was a government workers’ general strike/insurrection that was put down, but one of the most successful tactics was that the Minister of War was required to be a sitting or former flag officer. The military was small enough that that was a limited pool, and given that they controlled the promotions systems they chose their successors, and eventually the military-supremacy types got to a point where in order to form a government the parliament was required to install one of them and keep them happy lest they resign and force a change of government.

The final straw was basically the military deciding to invade Korea on their own initiative and daring the parliament to not support “our boys overseas”. The parliament blinked and that was that.