The biggest advances in the last 50 years have been in the field of optics. Today's (mil-spec) glassware is infinitely better than the stuff that WW2 snipers squinted through. Compare a Patt. 18 with a Schmidt and Bender. The real challenge is building sufficiently robust / "soldier-proof" / lightweight housings and mechanisms.
The .338 LM is not hugely different, ballistically speaking, than the .338 Win Mag or .340 Weatherby, both from from the early 1960s.
A 7mm? Anyone for a re-run of the .280 Ross! Remember that in WW1, a swag of "big-game" rifles were deployed, mainly by the Brits, for "bashing in" loopholes and other "armoured" features on the opposing trenchlines. The drawback was that every time someone cut loose with one of these canons with its VERY different muzzle blast, it drew a LOT of 7.92mm crabs. Thus, snipers so equipped, were not exactly welcome anywhere near the ordinary foot-slogger.
The basic 7.62 NATO is probably the most "refined" service cartridge on the planet. So what if the bullets go sub-sonic at about 900 yards? If you are harassing vehicles and signals installations, who cares? Being smacked in the chest by a barely subsonic 7.62 bullet WILL ruin your day unless you are wearing decent body armour.
The big "fifties" do all that a lot better and further, BUT, hiding the outrageous muzzle blast is a bit more tricky, especially in dry, open woodlands etc. Not only that, but even if the observer is VERY friendly with the shooter, steady exposure to that muzzle blast will cause health issues; a factor noted in several "official" documents. Silencers for the .50 cal? Yes they exist. Yes they work, but at a cost of a significant increase in bulk and weight: users would need a little trailer to drag the thing, and its ammo, around the place. Whilst re-tasked golf carts are handy on the target range, they would tend to stand out a bit on the two-way version.
Furthermore, ALL "mufflers" require regular cleaning and servicing; not something to be attempted whilst trying to look like the shrubbery or hiding in a muddy spider hole.
Yes, I know there have been some spectacular (and verified) shots in fun places like Afghanistan, and such "scores" represent "value for money".
However a light shower of 81mm mortar bombs does it further and much more thoroughly. For the average "digger", distance is good, more distance is better.