Except that even this best case scenario isn't true...
Think about this: What sets prices? The fact that there is (for example) only 1 hamburger per person created in the US per day. Currently, everyone has $1, and needs 1 hamburger. So the price is $1/hamburger. There is this rich guy, who has $1T, but he still only east 2 hamburgers.
OK, so now every has $1M. The rich guy is still fine, and he still buys his 2 hamburgers. But how many hamburgers can everyone else buy? Hm... there's still only one hamburger per person. So each normal person can still only buy one hamburger! So what is the price of a hamburger? $1M per hamburger!
OK, so you then say "well, there must be a huge incentive now to create more hamburgers, since people will pay $1M/hamburger." But here's the thing, at the end of the day, no one wants $1M, they want an extra hamburger. So since the number of "hamburger equivalents" you will pay per hamburger has not changed, there is not extra incentive. So nothing has changed, except that we just had massive inflation.
Poor people do not compete with rich people for goods, in general. Poor people compete with poor people for goods. Giving all the poor people $1M does not make them any better off, and it doesn't make the rich any worse off, it only destroys those that were on the cusp of breaking out of poverty.