Grandma's low property tax bill is not the problem per se, it is the punitively high property tax bill we charge more recently sold properties to make up for it. This is popular because it punishes techie migrants, but it also punishes downsizing late and life and new household formation early in life.

If we don't need the extra revenue from rising property values, we should cut property tax rates accordingly. City residents getting the same public services for a smaller percentage of their wealth would be an immensely positive impact of tech's prosperity.

If we do need it (and I suspect we do, because higher prices mean government facilities and staff are more expensive), we should collect it fairly across the board. Maybe "fair" means flat, maybe it means progressive, maybe it even means "tenure in city" or "tenure in neighborhood," but "tenure in current address" is crazy. At least use a mechanism with some thought put into its incentives and possible unintended consequences.