In short, this isn't supposed to happen.
One team isn't supposed to be able to amass 3 franchise players. The CBA, with the salary cap, trade rules, and lux tax, and the draft lottery, are all supposed to ensure that most of the time the top talent is disbursed. It didn't work, and it's worth paying attention to how these rules are supposed to result in a competitive league.
The main thing that all of these rules assume is that players will tend to go wherever they are paid the most. Under the cap, it would be pretty hard to have more than 2 max players on a team, at the most, without causing some serious cap issues. Of course, finding ways to add salary/talent via the various exceptions and trade rules is what being a GM is about at times. Still, the cap and trade rules are supposed to keep the top talent (and top salaries) from concentrating on one team.
Ditto for the draft. The suckiest teams get the best picks, and restricted free agency makes it most likely that teams will be able to keep the players they draft, since they can pay the most for the longest, thus making it most likely that the best players from a certain draft are spread out among the worst teams, and then that those teams likely retain those (presumably) top players.
But what we're seeing is that this entire game, rigged to keep talent spread out in the name of franchise marketing and competitiveness, falls apart as soon as a few individual people decide that an extra million or two per year (half of which goes to income taxes) out of dozens of millions coming in is worth sacrificing for the priviledge of playing on a superteam. Even without filling out their roster, half of the league has no chance of winning against Miami. Add Mike Miller, who is clearly sacrificing the most in this scenario, and now there are only a handful of teams that will probably be able to hang with Miami. If one or two more talented players sign on for the minimum, giving them the depth they need to go deep in the postseason, then it's lights-out. Next summer, they'll have the MLE and LLE to add to their roster. Look out.
It wasn't tampering that created this, but the basic assumption of all of the rules that make up a system that is designed to ensure competitiveness are based on players taking the most money they can. Wade, Bosh, and James have rejected that assumption, and the balance of power in the NBA has shifted for the next decade.