What, the prebate includes no adjustment for the differing costs of living in various areas of the country?
There is no way that that sort of favoritism can be all things to all people and I believe it’s better to offer the same prebate and let the taxpayers move if they think they’re in too expensive an area of the country for their income and consumption habits - or to change their habits.
Neither the government nor the other individual taxpayer owes those taxpayers you mention a living standard to which they’d like to become accustomed.