You say that, but it your counter is also obviously wrong. It would be trivial to have a system where everyone owns equal shares of everything - dissolve private property rights and nationalise. On the face of it that isn't a bad idea but when it is tried it fails spectacularly. I'm not aware of any surviving examples where equal ownership has worked without becoming hopelessly corrupted.
So in practice we know that some level of inequality which, if dropped below, does result in everyone being worse off.
As an interesting aside, ~90% of Canada is owned by the Crown [0]. It isn't obvious that this inequality is their biggest problem w.r.t. living standards.
> Back in reality some portion are pushed onto the street ... and end up dying
Yeah all that stuff does sound awful, but you are not going to the meat of what I was asking. Assuming we aren't creating new wealth (because that would be something that could be done now) then the wealthy will have to give something up so that the poor can gain. What is it? If wealthy people stop going on holidays then retrain the hotel receptionists as doctors? Are wealthy people taking more hours of doctor time than they need and so we make them live with shorter appointments?
I don't believe the wealthy are using enough raw resources for to make a difference; there'd need to be a massive redeployment and upskilling program training new people to have higher skills. That isn't obviously an equality issue, it might be an education problem or related to government healthcare policy.
> Only for the upper middle class does that mean they have just as nice a house in a less desirable neighborhood.
You haven't changed the number or quality of the houses, so you're basically suggesting the middle class and the poor swap houses. If the poor persons prior home wasn't an acceptable dwelling, why would it be acceptable to put a middle class family in it? Is there something wrong with the poor persons house? Is the issue that the wealthy are using too much building material so the poor can't do home repairs?