That simply isn't true. They only carry the local channels if they come to a carriage agreement with them. Most of them do, but they all don't. And even when they do, there are times when the contracts are up that the channels go away for a while while they continue negotiating.
As an example, a quick google search tells you that just yesterday Comcast came to an agreement with someone who owns a couple of Fox channels to get those channels back on the air after "a months-long blackout".
Or how about this article from last month:
Blackouts
"Now in September, we have seen this prediction become a reality as Comcast, DIRECTV, DISH, and Spectrum all have active blackouts affecting some ABC, CBS, FOX, & NBC locals."
In other words, another one of those things that you absolutely know to be true that is, in reality, not.