A 7MAG will make a mess of a lung shot on a Deer, but for Elk? there are many Elk who met a 7MAG and never went over the ridge.
The .3006 is a killer as a Elk calibre..165gr V-MAX.
I have never had the luck to draw a Elk permitt, but I know a few who used both calibres
and it worked just fine.
I will be the first to agree that there are many elk killed by a 7MM also by a .30/.30, 6.5MM. 257 Roberts etc.....lots of guns will kill elk. Many good elk rifles are range limited, and where I hunt, the ranges are getting longer as the elk get smarter.
I have killed several with an 06' myself (and have seen them soak up 6 or 7 bullets before going down), along with many killed by my 300 and 338. I moved up from the 06' due to range considerations and my personal experience has been that the lighter faster bullets whether out of a 7MM or a .30 cal Mag, have a tendancy to blow up elk, just the same as deer if you clip a shoulder or other bone mass before the bullet has slowed down enough. I have had the greatest personal success with the 338 and 250gr. premium bonded bullets resulting in 1 shot kills from 50 yds out to 600 yds with so little lost meat, that I have hung up my 300 WinMag(s) in favor of the heavier bullet.
I hunt the coast range of Oregon shooting Roosevelt bulls which are a good 30% heavier than the Rocky Mtn. version, with bone structure to match. Because of the terrain, we don't have the luxury of letting a bull go any farther after being hit than possible, "if they are still on their feet, we put more lead into them", so I stay with what works.
Several of my compadre's have hung up their 7Mags due to the explosive destruction they have experienced on what always turns out to be expensive meat even when you are able to hunt in your own back yard...Some of the newer premium bullet designs may help that some, I haven't had the desire to own one to know for myself, but I've seen many elk taken with 7Mags.
As with any hunting situation there is no single "right" gun except the one that you can shoot well, but faster, flatter, lighter isn't always a good match for heavy game.
Elk can be tough buggers, and the more you can slap them with on the first shot the better your chances are of having them stay put and not take you on a multiday/multimile hike through the woods.
My advice remains that when you finally draw that first precious elk permit, take a heavy caliber, you won't be disappointed.