The idea of rent suggests that you're paying a use fee to an owner. But if you live in a house that you own, and therefore lose the potential rental income, who are you paying that use fee to? Is the loss of potential income really the same as rent? Because in that case almost every choice/action in life involves a potential loss of income. There's probably always something more profitable one could have done with time/money.
> Is the loss of potential income really the same as rent?
yes it is. The term is called cost of capital, and sometimes imputed rent. But it's not an "expense" per se like it is when you pay liquid cash to somebody for use of a capital good.
if you then live in that house, you lose that rental income. That is what you are consuming. the rest of the investment remains intact.
as I like to phrase it, when you move from a rental into a house that you own, you still pay rent.