Colbert was almost certainly on track to be cancelled anyways. The program was tremendously expensive and was losing boatloads of money. I don't know if Trump accelerated the cancellation or not, but the writing was on the wall.

Indeed, it was just a smart move by Viacom/whatever to curry some favor with Trump by doing it now instead of waiting for another time, figuring that favor would be more valuable than the bad PR they earned. Probably a good bet since with the mergers (including the one they themselves were supposedly trying to push across the finish line) it's impractical to hold grudges for long. With only a few oligarchic firms in each industry you can't practically boycott more than maybe one at a time, and they all do shady stuff.