I owned a 338-06. It's about the simplest round to form brass for out there. Sexy round, and one that works great with a 22" bbl.
I've had a few medium bores, 338-06, 338 WM, 35 Rem, 358 Win, 350 RM, and 375 H&H.
Though some will disagree, I just don't think most of the lesser mediums do that much more (or as much) as a 30-06 loaded "right."
But "want" is not the same as "need," and the real-world has little to do with want.
Were I considering a medium anymore I'd go right back to the 375 H&H, or perhaps the 9.3x62. To me those offering something real over the 30-06, unless you get into the 338 WBY, RUM, Lapua, and other high capacity, high velocity magnums (no thanks).
I agree on the big magnums like the RUM and Lapua. They are just too much of a good thing. But, I do have a soft spot for the .340 Wby.