This seems not quite right to me. A Turing machine may always halt, but with time depending on its input size. The input can be arbitrarily large, so there's no finite bound on the state space.
My point, which I admit isn't very poignant, is that you can make an FSM that simulates a TM that only uses a finite portion of its tape. Yes, for some machines you will always be able to construct an input that exceeds what a particular FSM can do. When that happens, however, you can make a bigger FSM that simulates a larger (but still finite) tape.
This is analogous to putting more memory in your computer when you have a problem that doesn't fit.
This is analogous to putting more memory in your computer when you have a problem that doesn't fit.