In practice altering the distribution of wealth and income doesn't usually involve taking from A and giving to B. It usually is more taking from the rich and spending the money on free education and the like. You can also put taxes on large estates, give subsidised houses / loans to the less well off and so on.
There used to be quite a lot of that between WW2 and Thatcher getting in in the UK with tax rates as high as 98%. The period of this song https://youtu.be/pzU2owPegHE?t=23s
In general, if you subsidize something you get more of it and it costs more. Of course there may be some odd current in the river which makes this untrue - an example is bulk grain subsidies in the US, which prices risk of underproduction way down. IMO, this is like "if you need 4 GB RAM , get 8 just to be safe".
Indeed, in both housing and in education, we've subsidized it, there is more of it and it costs more.
Overall even the rich benefit from higher taxes if the middle class had more income today most of them would have been spending it on things the rich provide.
Today by squeezing the middle class and lower middle class they might be making money but over long term with the middle class having lower disposable income they will be spending less so hurt the higher classes as well.
There used to be quite a lot of that between WW2 and Thatcher getting in in the UK with tax rates as high as 98%. The period of this song https://youtu.be/pzU2owPegHE?t=23s