You do realize that it's quite easy to solve the halting problem in most cases, right?

The halting problem is unsolvable because _very particular_ (and pathological) cases are unsolvable. If a process is in a loop between the same instructions at the same states, it's very easy to tell that it's not going to halt -- the only challenge is that you can't make this determination for all processes all the time.

Mathematically, note that the concept of an oracle for the halting problem is well-defined (and a useful concept).

I was mostly making a jibe at the notion that there is a single, correct, and reliable method for identifying stuck/hung processes.

There are in fact fairly reliable heuristics for noting when things are going pear-shaped. The edge cases get sticky though.