I've shot thousands of rounds with JP "tank brake" as it's called here. I'd never use it on hunting rifle (although if one was installed on a rifle and it was all I got for hunting for some reason, I might use it).
You don't need to see your shot, and in some ways it's even detrimental. You must be able to call your shot. Cycling the bolt makes almost all muzzle movement irrelevant, you should be able to return from recoil much like clay shooters (with bolt manipulation added to the mix). It's only necessay to mitigate the recoil to a level that you will subconsciously ignore it. In heated driven hunt you might need to take shots at odd angles, e.g. sounder is coming close to your right but then changes direction and comes to your left. You cannot stomp around and change stance, if you don't want to spook them, anyway...
But the foremost reason is extra noise. You really need double protection (plugs and muffs) if you're going to purposefully shoot with JP. This means smaller margin of error for even single shots, say you have muffs on but your buttstock raises it and your ear is not protected. Also if you need to finish a beast, there might be dogs around etc.
BTW there are designs around that tame recoil better, in smaller package than JP. Especially true (and tested) for PRS rifles that resemble driven rifles much better than ARs that JP was originally designed for. Not that I'd use those for hunting either...