and also the statistics show that the checkbox for built second level is not popular (even I have stopped playing with it).
among the more sensible ideas already expressed for its rehabilitation were about changing the percentage ratio of the second level build for different towns.
does it make sense to do something in this direction?

I think it's not worth changing the percentage ratio. In any case, there are a maximum of 6 restarts, and a real result will only be visible with a significant increase. After all, there are few cases where a restart is taken specifically because of the absence of a built second level.
In general, the checkbox is a very convenient thing, in my opinion: we scribbled around and decided whether we need it or not. If there is at least one NO - the great random will decide everything. Games of Citadel/Castle/Inferno/Dungeon/Conflux not checking the checkbox = adding problems or a love for randomness (and it is these very enthusiasts who then cry the loudest that too few Hives were generated or too few stacks were given).