Austin has crazy property taxes in comparison to CA, which is where they get you.
2.5% tax rate evaluated for the property prices annually, so retiring on a fixed income in Austin is a tiny bit harder than in CA (that's the real goal of Prop 13).
Income taxes are easier to think about, because it goes to zero when your income drops, but property taxes based on the unrealized value of the house is completely out of your control.
The homestead exemption does apply, but Prop 13 is by far the superior option for an owner, though what Austin does is better for the government's fiscal policy.