I hunt with all sorts of stuff.
I've long preferred a semi due to the fact your next round cycles automatically and you never lose your hand positioning on the rifle, and for speed of follow-up shots. Reduced recoil is a nice bonus too, and it can be very noticeable on some models.
However, I do find that follow-up shots haven't actually been needed much in real life, and semi's do have some other, more minor things, that can be a little bit of a pain, like being more finicky about ammo that they like, and being a bit louder when cycling your first round, etc. The whole "maintenance" thing is so overblown as to be stupid, IMO; a fifteen minute cleaning once in the spring and once in the fall will keep 95% of semi's running like a top.
Levers are good too, but they also have plenty of parts that wetness, dirt and pine needles can fall into. No big deal really.
Bolts are more reliable than semi's or levers, but I have had them fail in the field too; nothing is 100%.
Failure rates on any well maintained action are generally super-low.
Singles, well, I consider them a bit of a speciality rifle for guys who just "like" them. Guys can hunt with them with tremendous effect, to be sure. I just don't know why someone would purposely chose a single shot over a repeater of any model, unless it was just for the fun of it or something. I tend to be a practical fellow, and I just can't see any practical reason to own a single; they aren't even cheaper than repeaters, which would be about the only reason I would get one, if they were dirt cheap.