When doing BIAB and I apply heat, I pull the bag up a bit, so it doesn't touch the bottom.
I don't lift it out all the way, just pull it up several inches. Plus I stir, since the grain is a good insulator and I don't want pockets of very hot water, that could denature enzymes.
If you have a false bottom, I think you still must be careful and constantly stir when the heat is on, and for some time after, as how water will be stuck on the bottom and want to rise, but be blocked by the grain bag.
Maybe something like:
Except this may not be safe, a sit's from China, and not SS.
I've read a number of BIAB brewers who mention the benefit of a mash out. I have not experimented, so I can't offer an opinion. But I would not assume it offers no benefit without some experiments to compare results.
I also think sparging (thus mashing less thin) and SCOOBing have a noticable impact on efficiency.