Polymath Tyler Cowen speculates thus:

In Cleveland [LeBron] is not actually expected to win, at least not right away.  They can play the young guys a lot and rest his legs and extend his career, while developing the quality of the overall team.  And if the mix of players somehow comes through in a year or two, he looks like a basketball genius …

Given their demographic structure and Bosh’s accruing softness, Miami is a contender only if it pushes LeBron very hard and thus shortens his career. I speculate that he was very upset that he was pushed and played so hard all year long, to rest Wade, only to develop those disabling leg cramps at the end of game one against San Antonio in the Finals, which caused him to lose face.

I haven’t seen other analyses take career length into account. LeBron is entering his thirties and watching the physical implosion of Kobe Bryant, one of his role models … He sees Wade — one of his best buddies — a broken player at age 32. Why not choose the outcome that might give him a few extra years of both salary and fun?

In other words, LeBron James updates his priors … In particular, he wants to avoid the fate of Dwyane Wade, a super-talented baller who, alas, now appears to be past his athletic-performance prime. (Wade is just 32 yrs old; LeBron, 29.) By signing with Cleveland, LeBron might be able to improve his image/reputation AND extend his playing career.

P.S. Happy Bastille Day!