While at the Infantry School in 1983, the tactical concept was to take the sling off when in the field. That's been over 30 years.
Tactical marksmanship isn't square range target marksmanship, and far too many confuse the two, attempting to impose what happens on a mowed grass field at paper targets with what happens from prepared or expedient fighting positions.
The target is radically different in size, too. Only 10's count in competition at the top ranks, and it's a small target. In combat, the target is a 18x18 center of mass - but the whole human body is a hit. A hit reduces the combat effectiveness of that soldier, hit enough of them the combat team is hampered, and with an advantage over the team, the tactical situation is usually won.
The Army teaches marksmanship - by their definition as assessed by the requirements of combat. Not by the arbitrary and artificial requirements of competition among equally skilled humans.
There is also the issue of moving over rough terrain, vegetation, or in urban infrastructure with all the embellishments of nature or man. A sling gets hung on a lot of stuff, at the wrong time, makes noise, increases motion, and attracts attention. Bad. The incremental increase in steady state accuracy is a minor loss compared to the major increase in mobility when you shoot while you physically move over obstacles. Those impediments to your travel also offer rests and can assist - something a square range has been deliberately bulldozed to remove. Tactical shooters use trees, window openings, car doors, etc. as a rest, if and when they exist for the short duration the shooter is there.
Once you shoot, you have to move. Try slinging up into any square range position, get off a shot, then move to another three seconds away with the requirement to hit the ground, then assume a firing position at least a barrel roll to one side or another. Do that for 30 minutes and I'm going to suggest that the first thing taken off the rifle is the sling.
It's NOT about marksmanship or a lack of it, it's about shoot-move-communicate - and to do the first two it's better in combat without the sling. Which is why you don't see it used overseas.
What we have today is a different battle doctrine - we don't dig in on trenchlines and snipe it out for a week at a time. It's mobile combat on foot or vehicle based - another obstacle to sling use - and what our granddaddy did in WWII is as out of date as what his did in the Civil War. What we have today is a lot of marketing, too, selling the AR nation competition accessories all dressed up as if it could be done tactically. And what we have today is just one soldier in one hundred citizens, so 99 of them aren't getting training and experience in actual combat doctrine, standing with their team mates ready to go out of the wire.
There's a time a place for a sling, it can increase accuracy. Be careful when and where you need to use it, and choose appropriately. It's not a one size fits all answer for every situation.