Pretty sure that in the NFL it is supposed to be used only to overturn demonstrably and clearly wrong decisions on the pitch. It is fair to say that it is used far more than that and they do use it to split hairs, but I think the original purpose has some validity. If it stuck to that, then I'd be fine with it. Maybe give the ref just one look at the screen - if it is obviously wrong then change it, if it is ambiguous then the on-field decision stays. I.e. it would be used to deal with hand of god things which are obvious; but not the 1966 did-it-cross-the-line stuff where you just stick to the original call.
If its influence cannot be limited to correcting palpable errors, then just bin it because it is shite as it is.