"Is there a perfect plains game calibre?"
Taking the bullet out of the equation and just assume premium bullets are always used, I like the 375 H&H for plains game. It shoots flat enough to shoot further than I care to shoot, it hits with good authority, and if you run across a monster buffalo while hunting plains game a proper rifle is already in your hands. It is also an "African" rifle. Nostalgia may not be important to some, but it is to me.
If dangerous game is not a possibility a 7 by 57 is on of my favorites. It can be built in a light handy package and has been used in Africa for well over a century.
Are either perfect? There are definitely more modern rounds that shoot platter and are lot more sexy.
However, this I can attest to, both my 7 by 57 and 375 H&H have been on some perfect hunts with me.