Taxing the rich is not offered as a panacea to solve all problems, and no one serious about the idea has framed it so narrowly as you have done.
One quite natural benefit, which you seem not to have considered, of taxing the rich, is beginnig to assuage the severe inequality that affords immensely imbalanced power and privilege to a tiny cohort of society.
Money is not a resource of fixed supply.
Taxing the rich is not offered as a panacea to solve all problems, and no one serious about the idea has framed it so narrowly as you have done.
One quite natural benefit, which you seem not to have considered, of taxing the rich, is beginnig to assuage the severe inequality that affords immensely imbalanced power and privilege to a tiny cohort of society.