I use 2 different psycho triggers depending on my bow -- selfbow vs recurve. But it works for me better than anything else I've tried. Anything that helps YOU hit the mark, is fine as far as I see things. The proof is on the paper.
As for hunting vs target shooting, I can't say as far as archery hunting is concerned (still working on that). But when looking at deer through a rifle scope, I've still gone through my mental shot checklist. Sometimes, I've gone through it all up to the trigger press, then started over back to verifying a secure rest because it didn't feel right the first time. I don't expect I would behave differently when using a bow. But I'll have to let you know.
Some of the older videos that advocate between hunting methods and target methods don't line up for me. Taking the methods of an exceptional shooter and applying them to ordinary people seems like a good idea at first. But you have to consider that those are ALREADY exceptional shooters. They may have done extremely well with ANY method they employed because they're already gifted athletes (survivorship bias, for the statistics nerds out there). In other words, for exceptional shooters, the method is often secondary to their pure, raw talent. It can't always be copied by average folks with the expectation of similar results. Sometimes it can. But it's not some sort of scientific law as it's made out to be. I suspect that some of that is just good salesmanship -- "You can do this too for only $19.95!"
I see clickers & other psycho-triggers as the average joe/jane's method to achieve good results if nothing else is working. Some folks can wingshoot half a dozen clays out of the air with their Benelli slung backward over their shoulder using a mirror or some variation of "the force." It's cool to watch. But nobody would ever recommend to teach that as a method to new or average shooters. Besides, there's no need to rush a hunting shot. If a deer is on the move, I'm going to let it walk. I learned that lesson many years ago.
If you're wingshooting discs or birds, well, that's different. Snap shoot away! I don't know how else you're going to do that. Marksmanship and wing shooting are fundamentally different activities. Hunting is not target shooting but employs target shooting at a single point in time during the hunt. But executing a precise shot is the same in both domains. However you best achieve that is just fine.