repaying a loan is not 'rent-like behaviour', applying a brush that broad would paint any regular payment as 'rent-like behaviour', which is preposterous.
'Economic rent' is a meaningless phrase, especially in this context. Rent is a concept of lease without ownership. We are literally talking about owning property. There is no rent. There is debt and burden, sure, but there is no rent.
Equity is not a lie. It's the very simple concept of a property's worth after deduction of amounts owing. Now the nuances and application has gotten insanely out of control in miltiple countries (I'm Australian, ask me about our multigenerational housing inequities!) But the basic idea of inflation increasing cost/value is generally sound.
A rental property and a ppr are nowhere near each other, not financially, socially or emotionally. They cannot be equated, no matter how much you torture the syntax. Each has their place for personal preference, but they are not the same