I hunted with an index release years ago, then went to a trad bow, and have picked up the compound again very recently. All of my hunting since December has been with a handheld release, and only one kill has been with a thumb button. The rest were all with a hinge.
I thought having a hinge being loose would be a problem but I keep mind in the front pocket of my bino harness and it's been easy to use quickly. I did buy a B3 Ranger with a wrist strap and thought I'd love the idea of the release being on my wrist, but honestly, the convenience was outweighed by it being a pain. It flopped around and hit my bow when I was trying to move in particular ways, and grabbing an arrow (or putting it back in the quicker) was really annoying. Definitely enjoyable to use in the moment, but after killing a few pigs with it I went back to my B3 Infinity Pro and shot a few other critters and I can't say the convenience of having it attached to my wrist made a noticeable and positive difference to me.
Currently got a UV2 stainless hinge on the way, and looking to trade my B3 Ranger for a Truball Abyss (my wife might use a thumb button). I'll keep my B3 Infinity Pro and either that or the UV2 will become my 'go to' release, but having said all that, I have a Stan PerfeX resistance release here that I shoot well and I may just hunt with that instead.
My point is, for me personally, I'm never going back to an index release. I like both my hands being free of anything when in the bush and I can quickly figure out other ways to hold a release.