While I can see why you are frustrated by the current set-up, and I agree that my players do get frustrated that one skill doesn't cover everything, I'm not 100% convinced. You seem to be assuming that this particular fantasy trope didn't invest in strength, dexterity, and both skills purely because it uses up resources that could be spent elsewhere and you would also like to spend those resources elsewhere. I get that, and the thief-acrobat is one classic subclass that I wish had been included in the rules. Without a subclass, I just think that covering those bases is more appropriate with a specialist feat. An Olympic gymnast isn't an Olympic long jumper but then neither are they an Olympic wrestler. Athletes spend a lot of resources specialising and feats can cover that. It's more of an issue that the feats don't cover it. It's as if they avoided it to preserve space for the acrobat subclass and then didn't follow through.
Generally, you don't fix problems with "here's a feat".
First off, the feat does not make you any better at those Athletics checks the game wants you to make. Nor does it circumvent having to do them.
Second, the solution "just use Acrobatics" is because the problem wasn't that a Rogue can't swim or climb. The solution is because the game makes that
too expensive. Asking you (and let's ignore what the feat does for a second) to take a feat is also expensive, so it doesn't fix the issue.
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Athletic heroes like rogues and fighters should be able to pop 'round the battlefield, neither being forced to take "the other's" physical skill just for basic movement - and more importantly, put precious ability points in an ability you're taking only because the game doesn't allow you basic movement with just one skill and ability.
(If you do like your Dex-build to do "pure strength stuff" such as grapple and make strength saves and lift gates and outcarry a pack mule, then by all means have at it and take Strength. But you shouldn't need to just in order to move just because the battlefield happens to feature fun three dimensional layouts, where your fantastic movement abilities are weirdly shut down by elevation differences. Especially since mundane jumping and swimming is nearly always eclipsed by magic when it really matters anyway. It's not that you gain particularly fantastic abilities. You mostly just patch niggling inabilities in your otherwise great repertoire of physical prowess)
If you already allow your Rogues to use Acrobatics to swing ropes or parkour their way up, you're halfway there. You just need to let go of the "well that's because there was alternative ways to pure climbing" mentality and realize that strength is part of all manners of elevation changes.
There is no such thing as "because there's steps and ropes you don't need Strength, you can do it with pure Dexterity." The distinction is silly, but more to the point, it's meaningless - it doesn't serve any useful purpose and indeed, all it accomplishes is cases where a Rogue player is shut down by some rules technicality.
Instead just embrace that martials are physically fit people. Some use one game stat and its associated skill; others use the other game stat and its associated skill. The simplest way of making the game work is to just say yes, and let people use either Athletics or Acrobatics interchangeably in the vast majority of cases
What you could do to incentivize doubling down on both Athletics and Acrobatics is use the "you have both the tool and the skill so you gain advantage" rule and say that if you're proficient in both, that's advantage.
It would mean that those of you arguing it's possible to think of an athletic hero without him being acrobatic, or an acrobatic hero without her being athletic, gains some satisfaction; all the while we solve one basic dilemma with how the vanilla rules work: there's just not enough incentive to take both Athletics (and Strength) and Acrobatics (and Dexterity). At least if you were assured of advantage (and didn't have to rely on making up fantastic descriptions for your DM to grant you advantage) it would be a small perk; maybe enough to justify taking both in some cases.
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