We are talkgin cartridges, not rifle, but a 7MM RM fits in a "standard" action size, same as a 30-06, and if you want a shorter rifle, that is easier to do than a longer one.
When you say "little" you are correct. 30-06 recoil is no popgun, you know you are not shooting a 223!
Yup, you won't see much difference in killing power...So why not go for the flatter shooting cartridge?
Id' say, at one time, with limited bullet and powder selection, the 30-06 was the most "versatile" but these days there is about a zillion contenders, from .308, 280, 280 AI (now a factory cartridge) 7mmRM, 300WSM.....Heck, even Rick had a good argument for the 35 Norma, since he coudl use lightweight pistol bullets to plink and make grouse loads with, and coudl use very heavy bullets for "stoppers"
The bottom line is that most hunters that own one of these cartridges can and will use it for everythign from yotes to grizzly bears, very few of them will use the more specialized bullets from the extremes of the spectrum, like the very light or very heavy ones...And all will do just fine.