Alrighty then,
3000 fps with a 175gr bullet is more than a little optimistic it's dangerously overpressure. But even if you could get a 175gr 7MM to 3000 fps out of a R7MM. Do the math and tell me how much point blank range you've actually gained over a .30-06 with 180 gr bullet leaving the nozzle @ 2800 FPS.
I'll do the math for you with similar BC bullets you've gained.....Wait for it.....About 50 yards further point blank range.
You're missing the whole point, and it is blatantly obvious.
Do you have any idea how difficult it is to find a 175 gr .284 bullet with a BC similar to a 180 gr .308 caliber bullet with the same style and construction?
The whole point is that the velocity advantage of the 7mm isn't all that great at the muzzle, but the larger average BC of its projectiles increases this advantage with range.
As mentioned, it's more fair to compare the .284 caliber 175 gr to a 200 or even 220 gr .308 caliber round in terms of ability to penetrate on game. And when you consider the velocity advantage the 7mm Rem Mag is going to have with a 175 gr bullet at 2900 (excuse me) fps as compared to the 200 or 220 gr out of an 06, the differences in trajectory become more appreciable.
Consider these SDs:
7mm 160 gr- .283
7mm 175 gr- .310
.30 cal 180 gr- .271
.30 cal 200 gr- .301
.338 cal 250 gr- .313
This means that in order to match the SD of the 175 gr 7mm, you have to go up to 220 gr .30 cal or skip .30 cal altogether and go with the 250 gr .338 caliber projectile. Either of these options has serious drawbacks when compared to the 7mm RM with the 175 gr bullet. The .30 cal with the 220 gr bullet isn't going to have near the trajectory of the 7mm round due to the fact that the vast majority of 220 gr .30 caliber hunting bullets are RN or semi-spitzers that lack both the BC and intial velocity of the 7mm RM/175 gr combo. And the .338 cal/250 gr combo is going to produce much more recoil.
Which brings us back to BC. Take the 175 gr .284 caliber Nosler Partition with a velocity of 2900 fps and a BC of .519 and compare it to the 180 gr .30 caliber Nosler Partition with a starting velocity of 2800 fps and a BC of .474. Heck, note even that the BC of the 175 gr .284 caliber Partition, flat base and all, is still appreciably higher than the 180 gr .30 caliber Nosler Ballistic Tip and Accubond projectiles, even with their polymer tips and boat tails. And of course, once again, that is the point--the BCs aren't similar. The velocities may be, but the BCs of most hunting bullets are, on average, very much in favor of the 7mm. So the velocity advantage it begins with is not the velocity advantage it ends with 400 yards downrange on the rib cage of a bull.
The only hunting bullet on the market that I have found that even really compares to the 7mm offerings are a couple of 200 gr spitzer boat tails, namely Sierra's 200 gr Gameking with a BC of .560 and Nosler's 200 gr Accubond with a BC of .588. And to really appreciate these bullets you have to step up to a .30 caliber magnum because the 06 isn't going to be able to push these bullets much past what, like 2500 to 2600 fps?
I don't have my external ballistics software here, so I am kind of handicapped in this debate. But run a .284 caliber 160 gr Nosler Accubond or 162 gr Hornady SST with a BC of .531 and .551 at 3000 fps (which I know to be possible because I have done it), and see how it compares with any .30 caliber load you want to run it against at .30-06 velocities.
I think that you'll find that a) you can't shrug off a 150 fps velocity advantage turning into a 300 fps velocity advantage by the time it gets downrange 400 to 500 yards and b) while not an earth shattering advantage in energy or trajectory, it can be appreciated and certainly, having that advantage at the expense of 5 to 10 grains more powder with virtually no increase in recoil is attractive. And again, on longer shots, velocity becomes crucial not only for its contribution to energy, but because it allows bullets to expand. Even if you have a .30 or .338 caliber magnum with a larger bullet driven at moderate velocities, any energy advantage these rounds produce is only going to be noticed if the rounds still have enough velocity when they get downrange to cause the bullet's to expand. Bullet manufactures often indicate this velocity threshold to be around 1900 fps. So if you have access to external ballistics software, compare the range at which the 7mm loaded with a 175 gr Nosler Partition at 2900 fps or a 160 gr Accubond at 3000 fps reaches this velocity threshold compared to your pet .30-06 hunting load, or even some of the .30 and .338 caliber magnum hunting loads on the market.
These, again, are advantages that aren't likely to be appreciable on the vast majority of hunting shots. But the OP has indicated the possibility of a 400 yard shot. While I am all for getting closer if it is possible, it is not always possible, and I am a firm believer that 400 and 500 yard shots on game by any reasonably competent marksmen should not be a problem. If it is within the OP's capabilities to take a 400 yard shot, and such a shot is a possibility, I think the advantages of a 7mm Rem Mag are appreciable.