One of the best gun writers and researchers was one Col. Townsend Whelen, for whom the .35 Whelen round is named today.
The late Col. Whelen was a very astute gun researcher and writer before today's idiots took over the pages of hunting and shooting magazines. Col. Whelen walked his talk and was a most interesting man, having a career and hobby of firearms from the .45-70 Trap Door clear through to the Garand and M-14.
One of his most fascinating articles was titled "Just a Little Bit More" and extolled the virtues of what you're saying: A 7mm-06, or .280/.284 bullet on a .30-06 case. It kicked a bit less, it went a bit further, it hit a bit harder. Col. Whelen's opinion was that if you had a perfectly good .30-06 or .270 Winchester hunting rifle, you should not bestir yourself to get rid of it in favor of a .280, but that if you were seeking one rifle with which you could hunt anything in the lower 48 states, a .280 deserved some very close examination.
After years of being abused by a .338 Winchester Mag and a couple of hunts with lighter .250 or similar rounds where a wounded animal walked off, I'm now in complete agreement with Col. Whelen: Something like a 7mm-06 would be absolutely ideal. The selection of bullets is outstanding, the ballistics are outstanding and the performance of this cartridge with modern powders makes the 7mm RemMag basically obsolete.
And, FWIW, I was recently flipping through the pages of one of these glossy, idiotic hunting magazines where they did an "efficiency" test of various hunting rounds, based on how much kinetic energy did one get for how much powder and recoil?
Guess what round came out on top?
The .35 Whelen, which is nothing more than a .30-06 necked up to take a .35 bullet.
Coincidence? I rather think not. There were no accidents coming out of Col. Townsend Whelen on the subject matter of ballistics. It is a shame that the current DOD people seem unwilling to go back and read what was written by one of the most fertile minds on ballistics the US military ever had.