We can use rifles for sport hunting of deer, but they are limited to .35 and larger cal and 1.16 to 1.8" case length.
"regular high power rifles" are legal to take deer under special nuisance permit, but this is pre regular hunting season and is a bit more involved.
"regular high power rifle" cartridges (like .308, .270 etc) are legal in handguns in the reg deer hunting season (.24 cal and up, min case length 1.16", no max...........bbl has to be 4" or longer).
The intent I believe is to keep the tooling to medium and short range. The exceptions being the larger rifle rounds in pistols or guys making wildcat cartridges for rifles............these folks aren't your average deer hunter, spend a bit more time and $ (usually) and as such, are not of the profile to jump out of a truck and blast away across a field at some 300 yard deer, not knowing what or who is behind it in the immediate or distant treeline.
Of course, we have some rubes who do that anyway.
But the average person is an idiot, doesn't matter if they hunt or not, or own a gun or not...........so IMHO the state has to play the odds.
Must say, a .44 mag rifle is a lot less punishing than a high performance slug from a 12 gauge and with hunting folks getting older, trying to keep them in the sport, and get new folks in, the "cheaper to shoot and less recoil stuff" is popular.
Back to hand "rifles".........or XP and TC stuff (and other) in rifle cartridges. Most of those rigs are scoped for longer distance and with an extended eye relief scope...........you are pretty limited in shot selection. Such rigs typically are for more "set up" shot scenarios. My bud runs a 7mm-08 striker to cover his dad's back ditch, 200 yarders, with hill backstop......he sits on opp hill on shooting sticks or bipod and dumps them when they stop.
Sitting in the deep woods and popping a trotter at 50 yards offhand, with such a pistol............might as well forget it. Rifle or shotgun with a low power scope and the shot would be easy.
Pluses and minuses to everything