Our computers deal with input though. That means hardware interrupts which in a Turing machine are basically equivalent to someone stopping the machine, writing the current state as a series of symbols in a special part of the tape, then writing some more symbols in some other place, moving the head there, setting the machine in a "interrupt handling state 1" and resuming it. Thousands of times per second.
I don't see a problem, the halting state was always an abstraction. Only the mathematical Turing construction stopped after it reached a result. Computers go on and work on something else.