Issue is what happens to retirees on a fixed income when value of their property increases?
That’s not specific to a land value tax, the same thing can happen with traditional property taxes when the property is re-assessed.
California tried to “solve” exactly that scenario with Prop 13 limiting how much the assessed value of property can increase without a change in ownership and it’s been a disaster (and a contributing factor to the housing crisis, albeit far from the only one).