Nope it isn't. Will it kill elk, Yes it will, but so will a 22 long rifle given the right range and right shot. Since 1963 I've killed better the 40 elk and I've seen a bunch more killed.
Sometimes the perfect shot doesn't present itself, sometimes the elk just jumps when you shoot, stuff happens.
Any legal gun will work, but most folks simply do better with cartridges designed more for heavier game like an elk.
I happen to like the magnums and shoot one of Remingtons old 8mm mags with a 220 grain spitzer boattail. Got friends here in Idaho and Montana that like the 06, various 7mm's, the multitude of 300 mags and on up.
Like I said you certainly can use the 25-06 and premium bullets will help, but if you ain't dead on that big bull can run to the bottom of frying pan canyon and you can easily spend days trying to get the meat out before it spoils. If the 25-06 is the top of your recoil limit then go for it and shoot straight, if not, well, it's still your decision isn't it.