no, if you paid off the mortgage, then the cost of your "rent" is just the cost of the capital sitting in the house (plus those maintenance costs you mentioned).
There's no such thing as free living. it is possible that rent is more expensive - but over time, this ought to normalize, as expensive rent will incentivize build-to-rent and arbitrage the difference to make a profit.
At most the portion of the rent I get from my capital is the difference between deploying the capital in the market and the return to housing. Since housing has historically beat the market that suggests a zero or negative rent for investing in housing.
this is not true unless you only start counting from the past 10-20 years, and only include regions that _did_ beat the market, rather than globally.
For instance, after paying off a mortgage entirely, my housing costs will be effectively repairs, property tax and utilities. That's a tiny fraction of rent. Meanwhile over 25 years property prices have more than tripled so it's likely the renter's rent would have gone from $1500/month to $4500/month or so. If you have $7000/month for both cost of living and savings then putting $5500/month into whatever assets you choose now that your home is paid off is going to generate much better returns than putting $2500/month into whatever asset you choose after paying off your inflated rent.
Alternatively, you can buy the home purely as an investment rather than a place to live. In this case, you have rental costs either way but you don't just make the capital gains on the home you also make rental income from renting it out. Typically rental income can be around 6% of property value. If you add that to the 7.5% returns to property YoY since 2001 you get 13.5% returns. You will have some expenses to deduct from that so your net returns might end up around 11%. That's still demolishing the stock market returns.