Earlier quoted context omitted.
All you say is interesting and probably true, but you did not address OP's specific point at all.
The OP's specific point was based on a misunderstanding: that being unable to pay the land value tax would mean they would have to move to a different city because the cost of living in their original city would be too high. This might be a reasonable concern during a transition to a land value tax system, but once the land value tax has been in place long enough to see more efficient use of land actually happening,…
No! That's not what OP said. He talked about the problem of _a change_ in the height of the tax on the same land over time and this making it become too expensive.
That's not the same thing, because while the land tax would not cause such a problem (as you correctly said) but rather improve the situation due to more efficient use, the problem of _change_ stays.