A couple generations ago, this would have been the easy option to use milsurp or sporterised versions of milsurps (Enfields, Mausers, etc).
Given the lack of available parts, support, antiquated optics mounting solutions, anyone opting to use milsurp in lieu of other available options would probably be doing it for nostaglia which is perfectly fine too. Might as well make use of what one has, even if it isn't the 'optimal' tool of today.
Not so, a lot of parts are available for milsurps, such as No1 and No4 Lee Enfields, same goes for Mauser 98s, and Mosins. Any gunsmith worth the title knows where to look/acquire.
Some of the more obscure milsurps may have such issues.
I see a lot of sportered milsurps, both at the range as well as in the field. Mind you, I tend to look at the firearms others are using.
I don't see many of them in the hands of the "under 30" crowd, but I don't see many hunters under 30 either.
No reason not to use your milsurps for hunting, as long as you, a shooter/hunter have done your homework and know how to shoot them, with good quality ammunition, or have taken the time to be sure the rifle is capable of good accuracy with the ammunition you purchase.
Many European firearms are still utilizing the Mauser 98 platform as a basis for fine hunting rifles. Some modify the concept slightly, with mostly cosmetic changes, but a lot of the parts will fit, without alteration, onto the old milsurps.
If you have a Remington 798, or a Yugo Zastava, they're pretty much the intermediate length 98 Mauser action, made in Serbia since WWI era, all dressed up for the part.