I have an old Remington Woodsmaster (semi-auto) in .243. It is not a range gun. It is a hunting gun. My dad (while he was alive) and I both used it. Each season we take a few shots for practice and to assure the scope is still at zero then it is hunted. As such, it likely has less than 250 rounds through it. It's never had a bipod on it; just a sling. We can shoot it 2 MOA or less without any issue.
Now if I were to go out to the range, put a 10 round magazine in it, and blast away then it would certainly burn out the barrel prematurely. That is not the use for which the rifle was designed. If you are a hunter, I don't see an issue with the caliber being a 'barrel burner'. Yes, the .243 can let a hunter down on larger deer - if the shot is poorly chosen. On big healthy Iowa corn feed deer, I wouldn't take a shot from the back quarters unless the deer were right on top of me. The .243 might still do the job, but I really don't care to spend a lot of time tracking. I like them to drop in a few yards.
IMHO the .243 is a hunting man's caliber and a fine one at that. It's not a range gun or one to use on a couple hundred prairie dogs in an afternoon.
I have a very nice bolt action 30.06. Other than for the pre-session checkout, it hasn't seen use for the last four seasons - because I just pick up the .243 and go.
I admit to bring a twenty-caliber fan, but I just don't see that you made the wrong choice at all. There is no perfect caliber. After all that is why there is such a selection. But there is a very good reason why the .243 has been such a popular round for so many years. It is a great caliber and you have a rifle that can give you many, many, years of enjoyment.