It's worth remembering that Sinclair and Nexstar cover only small fraction of ABC's potential nationwide audience, and that most of that audience reside in small markets. They have 56 of ABC affiliates in the 210 markets, but only 14 of them are in Top 50 markets, covering 8.6% of US TV households; while 14 more are in markets 51-100 covering 3.4% of US TV HH; and the remaining 28 are in markets 101-210 covering 1.2% of US TV HH.
So, 56 of 210 markets sounds like a lot, and it's not nothing, but grand total, the "ban" covers only about 13.3% of US TV HHs, which is fewer than the number of TV households in the New York City, Los Angeles, and Chicago DMAs combined.
It's because Sinclair and Nexstar focus on affiliates in small markets, many of those in deep ruby red areas, populated by people who probably didn't watch much Kimmel—or other late night talk shows—in the first place.
So in the final analysis, all this posturing by the companies is for the benefit of an audience of one, and by extension, for both the minions who work for him and the red hats who idolize him.