You generally need both good coaching and good players to win a ton of rings. Yeah, Jackson had Jordan, Pippen, Kobe, and Shaq. But those guys didn't win their rings until Jackson got there and didn't win any rings when he left. There was some stat web site that I ran across a couple months ago that tried to quantify the effect of a coach using various methods.
There are some things that are intangibles, like River's ubuntu theme that helped the Celtics bond, but things in the long run should show up in the stats.
Anyway, the conclusion was that among the top 20 coaches in the league, Jackson was ranked #1 in relative player performance. This means that while players were on a team he coached, their stats were consistently better than when they weren't on his team. It's been a while, but they also used another benchmark and Jackson ranked near the top of that one too.
I think the main effect of the coach is to motivate players to play near their max ceiling and to solve chemistry problems between crazy people, like Artest, Rodman, etc. Or you could say he just got really lucky 11 times in the last 20 seasons.
Lebron isn't moving to Miami. There's nothing there but ego problems if he has to take less pay than the others, and he won't like his legacy taking a hit saying that he couldn't win a ring until Wade dragged him along for one. Also, if he goes there, their roster will be those 3 and 12 draft picks and minimum salary guys, which makes it tough since those guys can't play 44+ minutes every game for ~100 games.
The only reason he would leave Cleveland is if there's another team with a great roster for him to slot into because Cleveland is his home and can offer him more money before the new CBA. Chicago/NJ/NY don't really fit the mold anymore without Wade or Bosh. Eh, knowing him, he could get an opt out after 3 years with his leverage so he doesn't have to sacrifice his prime if the Cavs can't get anyone to come.