Even if impeachment made it through the House, I doubt the Senate would hold him accountable.

I’d also argue that most establishment Dems don’t actually support impeachment. They view it as divisive.

I think you greatly overestimate what that power actually is. Most Americans know Sanders and AOC better than Schumer. Even if he has the name recognition and respect that some of the other party celebrities have, it would still be shouting into a void.

Being vocal isn’t going to cause Mike Johnson to suddenly put articles of impeachment up for a vote and there are not enough Republicans in the house that would force the issue.