I think you are slipping into the world of "oddball calibers" when you get to 7mm -- which is fine if you have a good battery of rifles in "normal" calibers, and a proper supply of ammo.
"Oddball"? Who's doing the defining here? The big 7 has been around since what, 1962? It's only the most popular belted magnum extant, at least in MY neck of the woods. It's extremely flat shooting, as light on the shoulder as the vaunted .30-06, yet more power downrange due to superior BCs in 7mm and superior velocity/energy at the muzzle. If the .30-06 can kill it, the 7 can kill it 100 yards or more farther down range.
When I was looking for another caliber than my .257 Roberts and thinking I might be going elk hunting in New Mexico with it, I settled on the 7 mag for the reasons given. I was seriously looking at the .284 as a 7mm alternative to the 06 (better bullet BCs) when I thought, why go .284 (aka 280 Remington aka 7mm express) when I can get the same gun in 7 mag and if I want less whop, I can down load it? So, I got a 7.
Well, full power, it's sorta too much for Texas whitetail. Yeah, it's got range, but I much prefer to keep my shots inside 300 yards. I'll push that a hundred yards if there's no wind and the shot is flat, perfect conditions, but rarely do I get a shot outside 200 yards, frankly, even out west. I did make a 350 yard cross canyon shot on a mulie one year in New Mexico with the gun, guess it helped there, bullet went right where I was placing it.
But, since getting that cannon, I've obtained a little Remington M7 in .308 and that's about all I use anymore. The little short action gun is light to carry, very handy size in a box blind or stand, marvelously accurate, and all the gun I need in Texas. I still like the 7, it's just a big, heavy chunk of metal and HUGE physically compared to the little M7 which, honestly, kills deer and hogs just as dead about as far as I am going to shoot.
I think if you walk into a gun shop in Albuquerque, you might find the 7 more popular there. It's a great gun for the western mountains where long shots can occur on big, tough targets. Down here in south Texas, the .243 is actually more popular and people even hunt deer with the .22-250, though I'm not one of 'em.
BTW, my 7 is an older M110 Savage and I don't find it kicks that bad. Hell, the thing weighs a ton. I did put a Ramline stock with recoil pad on it and I do use a Past recoil shield when shooting off a bench. In the field shooting at game, I don't even notice the recoil, frankly.