Were they sued before for spreading falsehoods? Really am asking here. There is a reason they believed that they would lose money if they continued to let him on the air.
What he did: Kimmel gaslit his audience with the standard, 'that kid that shot Kirk was a right winger', then made jokes about the folks grieving. I think the lie about him being right wing was the clincher if ABC has been sued in the past for letting their people lie on the air and has had to pay, they do not want to do it again. Mild threats from the FCC could be met with other responses, like having Kimmel come out and reverse his BS gaslighting, but they chose to go all in and take the man off the air.
FCC: Hey! Do something!
ABC: (Goes straight to cancel.) There.
FCC: thanks....
Out of all the choices they could have made, from the range of him coming out to apologize for his lie to him doubling down on his gaslighting BS they chose to cancel his show.