I’m a Democrat and also a corporate tax attorney.
You are grossly oversimplifying. Most corporations don’t sell directly to consumers. In addition and more importantly, a higher tax, like any other cost, may be managed in a number of ways without increasing prices and the resulting revenue.
All corporate profits subject to tax are the excess of revenue over costs. These are called earnings and profits under section 312 of the tax code. Higher taxes cut into profits, resulting NOT in a need to increase prices, but more directly in reduced amounts available for dividends under section 316. The first thing any corporation will do in the face of higher taxes is cut dividends.
Moreover, corporations CAN’T increase prices as much as they wish because if the have already set prices properly they will already have prices at a level that maximizes profit without reducing purchase volume per unit.