Correct. Assuming everything tracks over the long term with inflation (a historically accurate guess): mortgage payments stay nominally the same or shrink, rent goes up. This means that the cost of living goes down for owners while staying relatively the same for renters.

There is almost no long-term scenario where renting wins over buying in the long-term. It would require a magical multi-decade convergence of oracle-like investment ability and absolutely bizarre and sustained housing market that has no historic precedent anywhere in the world.