Landlords don't have infinite cash reserves. They still need to cover costs or minimize losses if they're betting on capital gains from property sale at some later date. Most renters pay for the maintenance and taxes of the property they live in, it's just not itemized for them and the costs are generally amortized and distributed among multiple tenants. Landlords are generally not charities, if you got lucky enough to find one who is, be very thankful.
You are correct that rent != mortgage and shouldn't be compared too close. Renting is a 100% loss, while mortgage is <100% depending on where you are in your repayment plan -- allowing the owner to recoup some of their housing costs after time.
After the mortgage is paid off, the renter still continues to loose 100% of their housing costs while the owner has only care and maintenance (and taxes) of the property to account for.