You could provide exceptions for a primary residence where the increased taxes would be sufficiently burdensome on the owner's income. Doesn't have to be all or nothing.
Just don't do what Prop 13 did in California where they applied the property tax limit even to commercial property for some reason.
You could also do what they do in Texas which is to allow anyone over 65 to defer any increased property tax amount (with interest) until sale or the death of the owner.
The California approach is to let the owner get massive appreciation, which they receive at sale, but never pay tax on any of it.
Does that ever lead to old people getting stuck? E.g., you've been getting deferrals for 25 years and now finally want to sell and move to be nearer family, but paying back the 25 deferred years and interest will not leave you with enough after the sale to afford a new place. And so you just have to stay until you die.
Michigan, for better or worse, does both. There's a major property tax break for your primary residence.
There's a Prop 13 style cap on property tax increases. It's the lesser of 5% or inflation. I'm not a fan of it, but it's not nearly as bad as Prop 13's low cap.
^ this. In Queensland, Australia, your family home (principal place of residence) is exempt and any other property gets no land tax up to a certain personal land holding value ($600k?). Once you go over the threshold, it's a percentage of value.
Just don't do what Prop 13 did in California where they applied the property tax limit even to commercial property for some reason.