If the rich were destroyed by being taxed out of existence and the overwhelming majority of that money went back into the hands of the people who created that wealth, pretending as though that would not benefit the poor is frankly an argument that can’t be taken seriously.
You are describing two separate functions that aren't related. The assumption that there is a finite amount of money to be distributed, and therefore distribution depends upon "getting" money from someone is in error.
By making this assumption you are ceding our dependence upon the wealthy and the need for them to remain wealthy enough to "fund" whatever payments you would wish the government to make to the poor going forward. You also set up unnecessary fights over such payments; 1) for the payments themselves, and 2) for the justification for taxing the wealthy.
Understand that I am fully on board with both punitively taxing the wealthy and providing far more benefits to advance the poor and middle class. I just know that our history of connecting them has not yielded the results we might wish. It speaks in the language of the oppressors who are happy to assume the role of our "source" for dollars and the dependency that generates.
The best way to deal with the accumulation of excessive wealth is to make it irrelevant to the needs of our society. This means charging our currency-issuing government with managing the nation's money supply to benefit the "general welfare" as mandated in our Constitution. Once the people see the correctness of that irrelevance I would just about guarantee the taxation of the wealthy will be much greater than it would be if they are viewed as necessary.