It really isn't. You could—and we did!—solve that problem by letting people defer property tax payments or borrow against their equity. California literally has a property tax postponment program for seniors. If we just wanted to keep people from being pushed out of their homes by rising house prices, we'd just expand that program.
The point of Prop 13 is to let people have their cake and eat it too: you get to keep the equity you gain from increased housing prices, but not pay the property tax that comes with them.