I hunt with detachable mag systems, I have never found them much of a hindrance. I'll explain my thoughts on it....
The mag sticking out the bottom has never been uncomfortable while slung, and doesn't get in the way while shooting off-hand, I either grab the front of the mag if I'm resting my elbow on my hip or hold the for-end. And even though 4 rounds is the most I have ever fired while hunting deer, elk, antelope or moose in the last 15 years I have been hunting them (since age 12), I still carry between 15 and 25 rounds for my primary firearm at all times, plus whatever I have for my sidearm plus spare mag/speed loader. This may seem excessive, perhaps it's because I have an irrational fear of running out of ammunition, I don't really know. But if I ever got lost in the back country, I'm sure I would be happy I had the spare ammunition.
Prior to having detachable mag rifles, I would have my rifle loaded, 10 or 15 rounds in a box in my day pack, and 5 to 10 loose rounds in my pockets in case I needed a quick reload. I tried ammo belts, and after loosing a couple rounds out of them, I won't use them again. Now, with detachable magazines, I have my mag in my rifle, a spare mag in my jacket pocket or in my stock pack depending on which rifle, and a partial box of ammo in my day pack. Makes it nice not having loose rounds in my pocket, and makes for quicker reloads if necessary.
Also, and this may be minor, but it makes unloading my rifle very easy. Drop mag, eject round out of the chamber. No loose rounds dumped out of the floor plate to have to deal with, don't have to push down on rounds to close the bolt, and I can easily do it with gloves on. I can unload an internal box mag rifle with gloves just fine, but it's easier with a DBM.
And with my DBM in a short action Remington, I can get longer OAL cartridges, which generally results in better ballistic capabilities and better accuracy with long range type bullets. And yes, you can get extended internal mag boxes and accomplish the same thing...I just prefer a DBM set up.
These are my reasons for choosing detachable magazines, but I'll add, I don't use the really long single stack 10 round mags. If I use a single stack type mag, it's 5 round. I just recently got a new set up for my heavy rifle that's an AICS type mag that is double stack single feed, and the 10 round mag is only 3/8" longer than my previous single stack 5 round.