Problem with that?
What if he breaks out of his psy-cell? And he would break out, eventually, because that's what happens in comics. And I think that Diana is genre-savvy enough to realize "You know how our villains constantly break out of the prisons we design for them, and escape from the interdimentional vortexes that are supposed to be inescapable? If that ever happens with Max Lord, then we're immediately back at square one, so do I really want to take that chance?"
What if it turns out that trapping him in the speed force or the Phantom Zone doesn't affect his psychic bond with Superman? It would be a small risk, to be sure, but once again, is it a chance you're willing to take when your mistake results in Superman killing you? Removing his powers might have the smallest margin for error, but what if he gets them back? Because that's also something that happens quite a lot in the DC-verse. Hell, Lord was bragging about how he had been digging around in Superman's head for years; what if it turns out that Max had brainwashed poor Supes so completely that Lord really didn't need his powers to control him?
Sure, Diana had other means at her disposal, but "just snap his damn neck" was the most obvious one, the most permanent one, and by far the most practical one.