Doesn’t the blanket statement that “raising taxes on companies doesn’t work” naturally imply that the only tax rate that “works” is zero?

Only if the product has completely inelastic demand? Also, that'd depend on the goal of the tax in question?

Raising taxes on income doesn't work. Workers will just demand higher wages to compensate.

If this logic doesn't work, then there are some unstated assumptions.

It works in the sense that some people feel better about paying higher taxes if they pay them by paying higher prices to corporations that then pay the tax.

And other people feel better about raising taxes on people if they do so by raising taxes on corporations that then raise prices on people.

There are some taxes that are actually designed to work that way - the most common instance being "sin" taxes on tobacco, alcohol, and cannabis as a way to reduce demand on those items by making them much more expensive.

That's the opposite of true in a monopoly environment.