Don't be naive. There was no jawboning from the previous administration to networks to cancel someone -- especially someone who always made fun of the President.
However, this is a a classic example of violation of 1A. (I agree that the thing that was probably in the grey area was they asked Twitter to remove certain COVID-19 medical disinformation tweets -- But, come on, many people were consuming horse dewormers for COVID and dying. )
The right's cancel culture is a violation of constitution because it's the government that's doing the cancelling.