If instead you are simply referring to the observation that physical computers have a finite amount of memory and thus we can solve the halting problem in finite time by simply iterating over all possible configurations, that is a somewhat uninteresting observation - since if we are already talking about real physical constraints, that algorithm is entirely useless for even the simplest computers from the 50s and 60s. It's basically equivalent to saying "any program will halt, because the sun will destroy all computers on Earth when it goes supernova".
More interestingly, it turns out that there are some finitist versions of the halting problem for finite-tape Turing machines, and they act as a similar kind of limit. That is, it turns out that the only way to verify whether an arbitrary finite-state Turing machine will halt on a specific input is to check all possible states (and this also requires a finite-state Turing machine with a larger tape than the one under analysis).
This result can actually be used in a very similar way to the infinite-tape halting problem: it 100% guarantees that, if your system is equivalent to a Turing machine with tape length N and M possible symbols, it will take more than N^M computational steps to check whether an arbitrary program holds. This can be used to prove that it is effectively impossible to check if a program halts, much the same as the "true" halting problem is used to prove that it is actually impossible to check.
For an example, an arbitrary program for a computer with as much memory as the infamous "640KB is enough for anyone" quote would require at least 640,000^255 (~10^1480) computational steps to check if it halts. So, we can just as easily say it is impossible to check and we wouldn't be far off.
This is very different from something like a total language (e.g. Idris) or a DFA, where it is actually possible to relatively quickly verify whether a program halts.