The 25/06 as is a fine case. Somewhat overbore, but pretty flat shooting type of thing. The Ackely Improved version is as well, just a bit more zip and has the shoulder. Next step up really is the 257 Weatherby. There are other larger cases with the 25 cal neck; one only has to peruse the net.
I believe that the 257 Weatherby is of course more over bore, but few really care. The case is all about speed. I would favor a 26" or more barrel, but that is just my perference, trying to get all the speed I can get. One might cruise the net for experiences with some of the later slow type powders.
One does not need to purchase factory ammo or factory brass for this case, if one has some reloading experience. I think the 7mmRemMag comes out a touch short in length when formed, one might watch the neck thicknesses as well, but everyone has their own thing about such. Other longer cases can be used to make up Weatherby brass.
To me, "want", trumps practicality. Will it recoil more than the 25-06?, yep; but is not bad to most in the properly stocked rifle. Barrel life will be shorter than the 30-06, but barrels are a dime a dozen; perhaps a worsecase? 500-1000 round barrel life is what you will need in your lifetime, if you are a deer/pronghorn or even coyote hunter. When the throat wears, set it back or buy a new blank; both approaches are available with a flip of the wrist.
I see that Remington is offering the 257 Weatherby in their 700 CDL? series from the Shot Show.
People that rechamber or move up from the 257 Roberts to the AI version will notice a recoil increase. Will it cause most not to try the AI?, probably not. Likewise, moving up from the 25-06 to the Weatherby; the prices of different types involved will vary from individual to individual. To me owning a Weatherby type chambering at least once in ones life, is like wondering what a Ferrari or a Lambo is like; never know until you try it for yourself.......