I sincerely have no idea.
The narrative that a leftist couldn't win is repeated so predictably and so often and by so many people that the whole idea has become sort of detached from reality, and there's no telling what would happen if it was actually a possibility.
And particularly since the one thing I'd pretty much guarantee is that the concerted efforts on the part of the ruling class to prevent a leftist from running would be as nothing compared to what they'd do and say in order to prevent one from winning.
No - I don't think they can.
Assuming they're at all sincere in the first place (with both Trump and Musk, there's no telling), they're all fired up about it now because they're still on the outside looking in. But soon enough, they're going to be in the same position as every other government body - they'll be cutting deals and making exceptions and trading favors and bowing to pressure and breaking promises and blame-shifting, and they'll fail and end up just another part of the swamp they claim they're going to drain.
The real problem though is the damage they're going to do along the way, since they're all ultimately just self-serving, lying sacks of shit - loathsome even by the already low standards of politics.