When I'm not playing Pathfinder, I'm running the Amber Diceless RPG, so believe me when I say that I love games that are low on mechanics, miniatures, and other fiddly bits. Amber is full-on immersion and storytelling (which requires a heavy dose of GM/PC trust).
In Pathfinder (or D&D), I think miniatures are vital to player immersion. A big part of the game is tactics, strategy, and how a character's abilities function in combat. Miniatures help to keep things clear in a tactical sense, thereby freeing the imagination to spend less effort trying to recall who is "fifteen feet away from the hill giant" and more on how deadly a swinging falcata looks or on the fearsome visage of a snarling lizardman.