I squat and DL in bare feet. A few times in flip flops. Get a better (for me anyway) grip on the floor and overall feel for those exercises. Even can help balance. I don't surf in shoes for the same reason I don't squat in shoes. Surf has been excellent, by the way.
Anyone who uses the shoe/boot that Olympic lifters wear can tell how they handle any leg work much better. The raised heels on them insure better control, balance and I might add, confidence. Also seems to affect the lower quads more, though you could squat on a 2X4/plates and get much the same focus. Of course wearing PL'ing shoes also has it's advantage. A friend of mine, who was in the 101st, would wear his old jump boots when squatting. Swore it added 20 to 30 lbs to his lifts. Good Luck.