I'm no expert but I think reentering at a shallower angle results in "bouncing off" the atmosphere. So, even if you did it multiple times like a rock skipping on water, you'd have to have extra fuel to counter the bounce "up" and go back down for each skip. Thus, back to the same "bring more fuel/weight to orbit" problem.
Any heat you see is velocity lost to the craft will eventually hit the atmosphere again. I think the main reason is that the skip and the second reentry is way less predictable than doing the descent in a single pass so for predictability of landing agencies much prefer to do a harder more controlled reentry.
