Other than the frame heating up with a lot of high-ROF shooting (and the polymer CCP frame is a better insulator than the steel P7 one) the only other major downside I can think of is the PITA factor of cleaning the gas cylinder with high-volume shooting. I don't think this pistol is necessarily marketed to the high-volume crowd, so I don't know how much that will be a factor.
One seeming advantage to the gas-delayed system is that it appears to have a certain amount of self-regulation built in: Higher pressure rounds bleed off higher pressures into the gas cylinder and therefore retard the slide more than lower-pressure ones. The recoil spring is stupid light and the slide is easy to run even for people with not a lot of grip strength. I've got half a mind to see if the gun will run with these weak-ass Fiocchi 115gr loads that stalled more conventional designs.
If they'd chamber this thing in .22 TCM, it would be gun hipster kryptonite. :D