I know the Creedmoor cannot do anything that other cartridges didn't already do, except that the marketing and factory support have rocketed it to popularity so that it available and easy.
For me, and in my opinion, this is the answer. It does nothing that others do not do, yet it has a marketing campaign that leads people to believe it is a do-it-all replacement for everything. An honest assessment is that it works as well as others, but has limitations, but this seems to get lost in the cheerleading. For your purposes it is fine, but I'm not going to spend money on "new" when I have already invested in others that do the same thing.
If I want flexibility, availability, and effectiveness for both hunting and targets, I have my .30-06. It's been answering the mail on all those things for over a hundred years, and I don't see a reason to change.
If I want to use a 6.5mm, the Swede could (does) work, but Gunny Highway put The Swede in his place back in the 80s, so I'm not in the market. Instead, I use my Mannlicher Schönauer 1903, keep it at reasonable ranges, and it is very effective for hunting. I also have a 1910 which is in .375, but the limitations on that cartridge are such that it can't do half what the '03 does. But it does have it's uses.
Where I do most of my hunting, I have no need to go larger than the '06, but if I did, the H&H version of the .375 would be my choice.
All that said, I find myself frequently in a situation where I can try all kinds of new chamberings. I could easily get a 7X64, or even a 7X57 or an 8X57. Others will occur to you. But I can't think of one that will do something the '06 won't, and focusing on one chambering makes my ammunition collection simple.