Another Pshat in that Gemara about Shlosha HKB”H Boche is the Maharal, that the crying is not a sign that he shouldn’t do it. On the contrary. It is like emotional tears from a meaningful event.
As far as the Mishna and its Meforshim are concerned, the Pshat is stated simply in the Bartenura that the problem is when you don’t have any income. There are references throughout the Gemara of the Tzurba Derabanan being supported by the Yeshiva.
I once saw that the Zohar Hakadosh says about the refusal to support Torah that it gives support to the Nachash (Amalek), that doesn’t come with its own bipods. Close to the war there were Gedolim that tried to rectify the situation by openning Yeshivos and programs. It was the most natural reaction to the war, in its aftermath, to rectify the situation and start Kollelim.