No amount of calibre or powder behind it will make up for outdated bullet design and bad marksmanship.
I bought a Stevens200 in .243 when they first came out. I used to hunt with my 40yr old Rem700 in .06. The .243 has shot eight deer ranging from 60yds to just over 300yds, all one shot kills using a 90gr bullet. I am extremely happy with it. I have also shot several yotes and have lost count of the gophers that have fallen to it.
As for moose, and I can`t prove this to anyone on here and don`t want to argue about it, but I know for a fact that my brother has shot(one shot kills also) over a dozen moose over the years in northern B.C. using his PH in .243,some at over 200yds.
So yes to your question about .243s being used for big game.
DF