Right, so by this logic when we see an elite Special Forces solider hauling heavy loads long distances, resisting interrogation, and hitting targets in dim light with his rifle at 300 yards, it's all down to his Strength, Con, Wis, and Dex and has nothing to do with his training, proficiencies, and class features?
Every single example you've put forward so far are elite, professional athletes. They're not lifting, running or jumping based on inherent strength alone. They've literally received specialized training over years, and are professionals.
Like our Special Forces solider, they would have training and experience (class levels, XP, proficiencies and feats) that contribute to the feats you are putting forward as examples.
In 5e with their shooting...no, it does not.
They only get a proficiency bonus between +2 to +6. That's a +4 difference, and EVERYONE gets that proficiency bonus.
A professor that hasn't touched a gun in their life get's that same proficiency bonus for training.
In 5e it kind of boils down to what your stats are that actually make the biggest differences.
If it was another edition...absolutely...but 5e sort of spits on the entire idea of skills making you actually a lot better than anyone else unless you are a rogue (and I'd think professional soldiers would be more of warriors/fighters/rangers than rogues and bards).
D&D isn't all that great as a simulation of anything, but 5e is worse at it than practically any other edition for doing it...IMO...simply because of how it pushes a bigger emphasis on ability scores rather than getting better mostly from experience and levelling.
In 5e (well, unless your DM does as the DMG suggests which means, most DMs don't) a bumpkin off the street who has a good ability score may have a slightly less chance of pulling off brain surgery than a neurosurgeon, and could have a good chance to succeed based on the D20 roll. In fact, if they have the exact same ability score as that trained neurosurgeon, they only have to roll 4 more than the neurosurgeon...maybe.
(PS: in reference to my above comment, the way I read the book though, which I mostly don't see it played at the tables run by others, is that if someone has a skill they can almost always succeed at tasks they do regularly and only roll for those which may be a challenging situation...and some skills others can't try to suceed at all even if they attempt it if they don't have the skill).
In AD&D, that Special Forces Soldier that was a Fighter at 8th level would have a +7 or +8 greater chance of hitting just based on experience alone, and possibly greater in melee if they had a high enough STR score as only Warriors got to have exceptional strength bonuses (anything that would give a +1 or greater to hit).
A similar situation in 2e and 3e. 4e was more on powers they were using, but as powers were class specific...well...