The rich can’t pass higher prices along, because if they could charge more, they already would.

They already have, and still are.

Obviously, they aren't going to jack prices up 5000% in a day, but 5% at a time, and all of a sudden we're paying a lot more than we should. It's been happening at a record pace, and we have no government mechanism to stop it.

And it doesn't have to be them jacking up prices, either. Replacing quality ingredients with cheaper stuff while charging the same. Or shrinkflation. These all adds up to people getting less, while someone else is getting more (money).

Cutting taxes on big companies doesn’t create jobs or lower prices – and raising taxes won’t destroy jobs or raise prices.

I agree with the first point, but the second point has been disproven by the fact that (in the United States) it does affect consumers.

"This paper provides evidence that corporate taxes impact retail product prices, and that a significant portion of corporate tax incidence falls on consumers.

and

"Approximately half of corporate tax incidence falls on consumers, suggesting that models used by policymakers may significantly underestimate the incidence of corporate taxes on consumers"

SOURCE

Increasing personal income tax on the rich may have a different effect, but simply taxing big companies isn't enough without protections to consumers and workers.