Thicker head gaskets also reduce quench area, the near-but-not-quite interference between the face of the piston and the flat surfaces of your cylinder head at the top of the combustion chamber.
Depending on who you believe, keeping the quench tight may provide anti-detonation capabilities due to epic turbulence created at TDC when the air and fuel mixture between the piston face and the flat parts of the head FORCE the mixture into the center of the chamber. The turbulence theoretically helps atomize stray "droplets" of fuel to avoid hot spots, and centers the resultant ignited charge over the piston center
rather than allowing it to happen at the "edges".
There's a ****-ton of theory out there about quench and its usefulness, and while I do not buy ALLOFIT, the basis of the theory seems reasonable. In my ancient, shitty Tiburon build, I had Ross build me a custom set of forged 9.5:1 pistons which only dished at the center where the valve reliefs were cut. I then decked the block so that, when cold, the quench distance between piston face and the flat pads of the cylinder head combustion chambers were 0.035". Stock quench distance in that motor was roughly measured at 0.065", give or take. Thus, my decking of the block combined with the very slightly dished pistons ended up with a compression ratio that was damned-close to the stock 10.3:1.
With the expansion of the forged pistons under load, with the piston "rock" from the wall clearances along with the terrible 1.5:1 rod ratio geometry in that motor, the combined movement + expansion of the piston resulted in something closer to 0.010-0.015" clearance while running.
I could feed that motor timing for days, and it got really good gas mileage.
It also had terrible blow-by because the piston-to-wall clearance was something absurd like 0.004" as defined by Ross for the power target I was aiming for.
That was probably way too much BlahBlahBlah from a n00b, but thought I'd at least offer.
I'd agree with the folks above; never go thicker head gasket.