Within capitalism, we could have some kind of system to provide equity to tenants. They are effectively already paying a mortgage (just not their own).

Outside of capitalism? Many more possibilities.

> we could have some kind of system to provide equity to tenants

This sounds interesting. Is this hypothetical? How does that equity get transferred/slowly leaked to the next tenant? How does one liquify it?

I don't know how such a system would work exactly, but I know it would require that we stop treating houses like speculative assets and start treating them like a basic need (shelter).