I'm A Banana
Potassium-Rich
First, Jack of All Trades comes at second level. Remarkable Athlete comes at 7th.
Yeah. I mean, we can't really examine these things in isolation from other class abilities, but RA is clearly weaker. It just doesn't seem nearly as pointless as it did at first to me. So I'm giving that initial assessment of mine a second thought. I don't think it's quite as weak as it seems on paper. "+2 to Str, Dex, and Con checks" would have been almost empty in 4e or 3e, a non-nothing bit. It seems like that may not be the case in 5e in practice.
Second there are such a thing as skills.
A "Remarkable Athlete" can never be a superior athlete. Either they are trained in Athletics (in which case they get diddly squat for their athletics from Remarkable Athlete) or they are a second rate Athlete (in which case they are decent - but not as good as someone with a skill proficiency in athletics). Likewise Stealth.
That's the same thing a Jack of All Trades will face. My Minobard will never be as good at Investigation checks as our party's INT-monkeys. I will not be as good as a specialist.
However, being that good isn't necessary. Bounded Accuracy means that even nonspecialists have at least a moderate chance of success, and half-proficiency significantly improves that moderate chance. It also shores up weaknesses -- though this is probably more common to experience with Jack, one of the things I noticed was that I no longer make any active roll with a penalty.
While I'm never going to be the first choice for seeing through an illusion, I can certainly help, and if I find myself in a situation where for some reason I'm the only one able to make the check, or if I am for some reason forced to, I will not be dead weight.
Remarkable Athletes will never be the first choice for Stealth in a party with a Dex-monkey rogue with Stealth expertise. But it's not really necessary to be at or even NEAR that level of skill to be able to participate meaningfully. This isn't 3e or 4e where if you don't have the highest skill bonus in a party you might as well not participate. Every +1 does count.
Most out of combat rolls are in my experience skill rolls. And Remarkable Athlete only puts you in the band of "The person you call on when you do not have someone trained in the skill". Because Skills are a thing. It helps one of your saving throws (which is good) - but you're already proficient in the other two physical stats.
The interpretation is that this language helps saving throws, too? Huh, I was reading that it doesn't (a check as distinct from a save).
Maybe my bard just got a little more awesome.

Second, even if we were to accept your claim that it gives you a bonus on half your out of combat rolls then it would only do so under one specific circumstance. That all your trained skills were mental skills. And this is where being seventh level makes a large difference. Either as a fighter you spend your first six levels untrained in physical skills (which is weird) or you retrain - and take a penalty to all the physical skills you retrained.
Remarkable Athlete is significantly less than half of Jack of All Trades.
I dunno how many fighters are trained in every Str/Dex/Con skill (Though an Urchin Fighter could pull it off!), but the chapter on using ability scores specifically mentions that not every check falls under the camp of a skill, and includes examples for each ability score, such as forcing open doors, breaking free of bonds, squeezing through tunnels, hanging onto a wagon as it drags you, tipping over statues, stop rolling boulders, steer a chariot, control a cart, pick a lock, disable a trap, tie a knot, wriggle out of bonds, play an instrument, craft an intricate object, hold your breath, endure a forced march, go without sleep, survive without food or water, or drink a lot of alcohol quickly.
That doesn't exactly seem marginal to me.
While my experience in 4e was that most noncombat checks were skill checks, I don't know that this remains necessarily true in 5e. "General" skills like Endurance and Thievery were dropped, and I'm thinking this is intentional. Skills seem to be much more specific, and much more about getting more reliable successes.
I'm still not convinced that Remarkable Athlete is good enough, but I wouldn't write it off. You don't need a +4 to compete with someone who has a +6 in 5e, and people won't always be able to apply that full bonus.