I see your reasoning here, and I don't disagree - but I would add one more piece to the plot . . .
if by increasing your prices because of increased taxes you would cause your customer base to abandon your product (for something cheaper) then you might have to reconsider how much profit you would have to make.
So if someone else with the same product and the same quality of product is willing to make less profit, they would conceivably get a bigger part of the market, and thus could put you out of business.
So it is possible that increasing taxes on the rich could cause them to have to reconsider their profit margins.
You do not seem to know how this works for a small business man.
If the government raise my taxes by $6,000 in one year, this is how it would be passed on to my customer---
I have about 10,000 transactions a year and each transaction is $100 so each transaction would only increase 60 cents or 0.6%.
Most people wound never realize the increase.
My taxes would go up $6,000 and the customers would pay the increase without even realizing it.
But, I never raised prices until my competition did, and they always did when cost went up.
Need to also understand, at some point, a small business owner will come to the point where the hours worked and the investment involved is not worth it so he just closes up, goes to work for someone else.
That puts people out of work, lessens competition, which leads to even higher prices.
If people want a socialist state, just understand that YOU will pay for it with YOUR money.
Every socialist state still has the rich. And those rich will continue to get richer at the expense of the consumer.