*And, before anyone starts complaining about something for nothing paid for by 'taxpayers', I'd just point out that even people who don't pay income tax are taxpayers; nearly everything we purchase has a tax element.
I could also point out that tax doesn't fund government spending... zzzzzz*
People might not get the nomenclature right, but the principle is that on the whole, people don't like to see others getting for free what they have had to work for, and I understand that way of thinking.
Also, it may well be the case that everyone pays purchase tax, but if someone hasn't earned the money from which it is paid, it is not quite the same as for someone who has earned, been taxed and is taxed again on purchases. It's not just about money, it's about contributing to society, but that's a whole different argument.
My thinking about rents and caps is that if landlords are not making a fortune from renters they will sell the houses, thus increasing the number for sale, and therefore the prices that everyone (but particularly young people) will have to pay.
It would possibly also even out the differentials between geographical areas. If renting in London cost the same as, say, Liverpool there would be more geographical mobility, and fewer 'hotspots' which price out anyone who has not (or whose parents have not) made a fortune by buying a discounted council house or being lucky enough to buy on the open market in an area where prices have rocketed.
As I'm sure is very clear, however, I am not an economist or an expert in housing or benefits. I am just offering my thoughts on what might make for a fairer society.