They sort of already do, it's just done in the background. If you blow too many calls, you just don't get to ref. last night we got the best of the best and I thought they were extremely fair (and at times I thought they were in the spurs favor).
Also how does a home team getting to bring their own refs make things fair? Do you think we would win any game in LA if this were to happen? This would just ensure that the rich always win unless you made the fine ridiculous. If that happened, what happens when a poor teams refs blow a call? The system we have is like democracy, it may not be the best but it's the best we've got.