The .30-30 remains the #1 deer cartridge for over 100 years for a reason. Even today it outsells many better cartridges and takes deer. While it can be faulted for not being a modern flat shooting bullet launcher, it hasn't seem to deter hunters from using it at the ranges they take deer at.
Why increase the amount of recoil by moving to a larger one? It's a fact shooters will anticipate harsher recoil and shoot more inaccurately, or less often. There's little to be gained by forcing yourself to carry guns that have to be at least a pound heavier to handle the bigger power loads, and trading down to the lightest manual action means not getting second shots rapidly or accurately. And if you're honest about it, you've heard hunters emptying manual actions pretty often.
Intermediate calibers do the job, although I won't go so far as to recommend 5.56. For hunting, the 6.8SPC is a perfect match, shoots flatter than the .30-30, carries 1000 foot pounds further than most hunters would attempt - 350 yards - and has little recoil in comparison to the big cartridges invented half a century ago. Put that in an AR15, and you have more power than the .30-30, better range, flatter shooting, a flattop receiver that accepts almost any optic ever designed, light weight, and is the easiest to take down and clean practically ever invented.
With a five or ten shot mag, often required, you can unload quickly when needed, and with a lot less jacking the action - which is very commonly the situation with negligent discharges. The forward assist actually has some value for the hunter in the field, it's the one time you can ride the bolt forward and then quietly lock it. Advanced hunters have noted game does understand that truck doors slamming and actions getting racked mean time to get under cover - just as much as if you heard it in your front yard.
Of course, not everyone wants the stigma of carrying a military rifle, especially one with an actual history of being durable and easy to use. It certainly didn't help the Mauser, '03A3, Arisaka, SMLE, Enfield, Mosin Nagant, Garand, M1A, or a dozen others when hunters wanted something that could take some abuse in the field.
But since hunting isn't a fashion parade, I've not let it bother me - my first hunting rifle was an HK91 with first generation Aimpoint. It got deer, and the 6.8SPC will, too.