You're missing a big point of buying with a fixed mortgage though -- its partially a hedge against housing cost inflation. Sure, property taxes will go up as property values increase, but taxes aren't really that large of the total housing cost of my home. Taxes could double and it still wouldn't be the majority of the cost of my house. Most of my monthly cost of my house is P&I, values that won't go up.
My mortgage, insurance, taxes, and savings towards repairs is now a good bit less than the current rent at my last apartment just a couple of miles from my house. But my house has over twice the square footage, a private garage, a private yard, etc.