I think he'd hang with Shogun honestly, given Shogun's own deteriorating physicality and tendency to brawl. I think Machida would beat him, as would Jones and every wrestler with a decent chin. I think Rashad would get caught in a three rounder, and consequently finished, but would dominate in the grappling aspect. Davis would beat him, Bader would lose, Gustafsson would lose, Lil Nog would lose.
So all in all, I think he'd be more competitive. World beater? Probably not. Not in that shark tank. But more competitive than trying to hang with guys that have 20-40lbs of lean muscle, reach and height on him, and are developing games that nullify his own. I just don't see Cain losing to him, or Reem, or Junior, or Barnett. Too big, too skilled at grappling and top control. At LHW one of those problems go away (mostly).
But you have a point. Why move down and be a fringe contender, when you could try to revive yourself in the division you spent your career in.
As a side note: I think the guy would benefit greatly from training with a high level BJJ guy. Fedor and his camp never took the idea seriously though, even when his game from his back started becoming an issue back in 08. Hell, they didn't want to pay Magalhaes to train with him. A case of crazy Russians I guess, hahah.