Because it is stating that the government should control private behavior, which bumps into free speech and freedom of association issues. That gets pretty controversial.
There are other solutions to the stated problem:
> Given their market dominance, they should absolutely not have any right to refuse service.
The fix is to address the precondition in that statement: their market dominance. If a single entity is so powerful that it can control entire markets, then the problem is not what it does with that power, but that it has that power in the first place.
The solution to this problem is enforcing our existing anti-trust laws, not passing new laws to compel private behavior. We should not have only one or two entities that control this entire market. That's a sign of a broken market, and that's what must be addressed.