Remember I mentioned squish and quench, these are functions of that flat side of the combustion chamber. Both of these functions are aided by as close a closure of the piston's deck to the head's deck as is possible to achieve within mechanical limitations.
First in the compression cycle squish happens as these two sections close on each other. This drives the mixture in this area back into the chamber by the spark plug with great force. The resulting turbulence and high density makes for a fast and complete burn when the plug ignites it. This reduces the amount of timing lead which reduces early forces in the combustion process that want to drive the piston back the way it came, which results in power lost. It also delays peak cylinder pressure and temperature to a moment when the piston is headed down the bore in the proper direction. This effect is to reduce the tendency to detonate.
The second event after ignition is that the close proximity of the piston and head decks perform what's called "quench". This is where the hot end-burn gases that like to detonate are trapped between two relatively cool surfaces with a lot of area compared to the volume. This sucks a lot of heat out and prevents detonation.
A third feature of modern heads is the beak that protrudes from the squish/quench deck between the valves. This helps prevent incoming mixture from being sucked thru the exhaust during the cam's overlap phase. The result is a denser mixture upon compression and more power and efficiency. Of course this dampens out the rough idle of a big cam. But it trades the rumpty rump idle for more power, better fuel economy and lower emissions.
Now if you have a flat top piston with a .040 inch clearance on the squish/quench side, the effects of squish and quench are maximized by how close the piston and head deck close with each other. The effect is the same with a "D" dish piston where the dish is all under the valve pocket. However, a piston with a circular dish cannot close any more than the raised rim of the piston crown. So even if this crown is .040 inch away from the head's squish/quench deck the floor of the dish is a considerable distance away and it cannot and does not expel the mixture toward the plug with sufficient force upon compression to throughly agitate the mixture for the most effective burn. At the post ignition point, it does not provide the high surface area to volume ratio of a flat top so that the late burn's excessively high temps are not damped. Both of these conditions lead to reduced power as on the squish phase the burn is slower and weaker requiring more timing lead which has the effect of first trying to drive the piston backwards and second increases cylinder pressure and temperature too early which combined with inadequate quench leads to detonation and preignition.