You can definitely spend less when your mortgage is paid off.

But I'll admit that part of my reason for buying was to prevent the situation where I might be living on a fixed income some day, and having my rent go up every year. That seemed like a good thing to try to prevent.

Buying a house requires a high monthly payment, which remains constant over time, and one day ends. Renting requires a high monthly payment that rises over time, sometimes unpredictably, and never ends.