First and probably the most important thing is that1.6mm PCBs are the standard and I havent seen 1mm thickness available in all of the sites Ive been, 0.8mm is the closest one. Being that thin also may lead them to break easier.
Also most of the boards use a plate which is where most of the flex in a board comes from and the PCB just kinda deals with it. Ive seen some boards use the 0.8mm PCBs so its not impossible to use them or something new, but honestly I dont think that changes the experience in a big way.
This is based on my view and experience, its not "rough data" by any means, so you might wanna use my points just to think about it.