The owners were already mad about the "superteam" issue, if superstars take that much of a paycut to sign more talent that's going to get even worse. Now you have the union and owners both angry.
I'm not saying there can't be some bit of a paycut, but too much just won't happen.
And when we say they took a cut to be in Miami, lets realize the tax breaks of that state.
Owners I'll give you, but they're really powerless to do anything as long as the current CBA is in place. Still I don't understand why the union wouldn't like it. It won't devalue the market, it would mean more money for other players, etc. (which I mentioned above).
Why specifically wouldn't the union like it?
There are a range of players that make the max. The Union likes that (obviously) and yes, even if LeBron didn't make the max there are players below his skill that would. However, it just doesn't set a good precedent, like I said before.
Obviously say a player like Rondo still gets a max contract on his next one even if LeBron takes less, but over time maybe that goes away if you see people taking discounts. The players union is there because players and owners aren't all friendly and have different goals. Players don't want to start giving up salary as a group. If that was a pattern that kept having over time, eventually I think salaries would go down. If I was an owner and saw the top few players take discounts I'd look at a Rondo and say "but this guy is worth the max? Nah" and I'd let him walk. And that sentiment would grow.
Look at the NFL this year. Many think the owners colluded to bring the free agent market down in a big way. Cliff Avril was a FA and it was thought he would get a 5 year contract for huge money, but he ended up going to Seattle for 2 years and not much. Yes I'm sure part of that was he wanted to be on a good team but the market wasn't there how he thought it wasn't going to be. There were a bunch of examples this offseason.
I'm not saying it couldn't happen that LeBron gives them a bit of a discount, but it won't be much. It only happens in Miami because in the end they are making at least as much (probably more) than they would at the max elsewhere because there's no income tax.
Between all the factors, this is why you don't see stars take big discounts. Owners and the union both have reasons to push against it for their own reasons. I think the owners would be the first group to riot if that happened (and for good reason, the coat tail riding is already extreme for lower level players, if it extended to stars that would be too much).