That is gaming the definitions of "states" a bit. Your example has a official finite number of "states" combined with an unbounded tape of extra states while only counting the FSM controlling it. That tape is part of the state, the machine can edit / read the tape in its decision procedure.

Noting this a few more states than a handful are possible. For example my laptop with bitpacking could track the visited or not visited flag for 64000000000 states without even using disk. Tracking a 33 bit FSM.

I agree though that linear bounded Turing machines having a solution for the halting problem is not actually that useful for real computers considering by the time a few registers had been iterated over the sun would have exploded.