You are basically describing this[1][2][3] and it's not really that great at anything in particular (especially not military use) and are primarily used by people who want to shoot a trophy buck that's 400yd away. IMO they're kind of the hipster beer of the rifle world. They do little a boring old Bud won't do but they sure put a bigger hole in your wallet.
Read up on the history of intermediate cartridges[4] and assault rifles (not "assault weapons", the former is a technical term, the latter is anything but). Earlier intermediate cartridges (were a standard size .30-ish cal bullet on top of a 30-40mm case instead of a 50-70mm case of a traditional full power rifle round. Later intermediate cartridges such as 5.56x45 and 5.45x39 (the Russians stuck a smaller bullet on top of the 7.62x39 cartridge) stick an even smaller bullet on top of an intermediate size case because the smaller bullet going faster does the job just as well with less weight (I'm painting with a really broad brush here). These 2nd gen intermediate cartridges are what I think you're getting at but you're hung up on the rifle cartridge. For simply killing people 0-350yd away you don't need that much bang, it's actually detrimental because it's extra weight and makes the firearm harder to handle.
You also need thinking in terms of energy. All the energy in the world is useless if you can't transfer it to the target properly. It doesn't take much energy dissipated in a human torso to immediately incapacitate and kill. Better understanding of the needs of combat troops and nature of engagements and terminal ballistics is what led to the switch from intermediate cartridges starting in the 1940s.
Of course you have to remember that everything is still a trade-off in cartridge design and the nature of the engagements you expect still plays a large role in what the "best" tool for the job is and often the difference is only marginal at best.
[1]https://en.wikipedia.org/wiki/.270_Winchester_Short_Magnum
[2]https://en.wikipedia.org/wiki/.270_Weatherby_Magnum
[3]https://en.wikipedia.org/wiki/.223_Winchester_Super_Short_Ma...