There's a lot of spin around this, used to distract everyone from the truth.
One important aspect: out-of-work benefits are a tiny proportion of the overall benefits bill. Most of it goes to pensioners, and much of the rest to people who are in work but on poverty wages that don't cover essential outgoings, like keeping a roof over your head.
Another key point: the 'savings' generated by this scheme will be minimal in terms of the overall welfare bill. And largely illusory, as the costs will just crop up elsewhere in the system - it's far more expensive for councils to dump families in B&Bs than to pay housing benefit, to take just one tiny element of this mess. This policy won't benefit taxpayers in any way at all - it will very probably end up costing more.
Another important fact: the cap applies to households, the 'average earnings' figure the government is fond of quoting applies to individuals. They aren't comparing like with like - they are twisting the facts. (And people in work on low wages who have families are entitled to in-work benefits such as tax credits, so the total household income comparison is flawed in another direction as well.)
Another fact - there is a severe shortage of social housing and affordable housing, while rents are at record levels. This is not the fault of people who just want somewhere to live, and I'm not sure why they are being punished for the dysfunctional housing market and the failures of politicians. Well, I can guess, but I don't know why anyone who isn't a member of this government is prepared to fall for it.
I'm lucky I've got a mortgage and have had one for donkey's years - I couldn't afford to rent. I really feel for people who are stuck in expensive rented accommodation.