Sure, but that's demonstrably more to do with the actual financial position than the ownership status. If you own the house and no longer pay a mortgage then you're ipso facto wealthier — although you presumably do still pay property tax.

During the period of the mortgage, while rent wouldn't necessarily be cheap, it would be cheaper than the TCO of the house. The overall financial consideration is complex and pro-ownership dogma is just dogma: see e.g. https://www.youtube.com/watch?v=j4H9LL7A-nQ. More importantly in my opinion, though (and especially for single childless people), rental housing is available in smaller and finer-grained quantities.