Ugh. I'd written a longer reply, but it got eaten. I'll try for shorter this time.
It's quite telling that your analysis focuses entirely on combat. In the fiction referenced there, combat is handled by the fighters and at times by Gandalf--that's not the area where the hobbits make their contribution.
I...didn't focus entirely on combat. "Skill checks that Aragorn finds challenging..." is talking about skills and not combat, right?
And saying the hobbits don't contribute to combat pokes a hole in your "the hobbits can meaningfully contribute!" statement. "They can contribute...as long as they avoid all the places where they can't" should be true of all games ever. You can have any color you want, as long as the color you want is black. Catering to the minimum-level players by shielding them from the things that would hurt them or challenge them doesn't make 5e any more friendly to highest-and-lowest mixed parties than any prior edition of D&D. (Nor, for that matter, does it make 5e any less so.)
Let's say the hobbits have proficiency in Sleight of Hand and Deception, with Cha 14 and DX 16. They'll have +5 to picking someone's pocket where Aragorn might have +2 (he seems like a melee type to me), and they'll have +4 to attempts to talk themselves out of trouble when they're caught. The fact that Aragorn has +8 or +9 to his own best skills (Athletics, Stealth, Nature) is beside the point--the hobbits are contributing. If proficiency bonuses were a massive +1 per level or something, this would cease to be true, and heterogenous levels wouldn't work.
If we're adhering to the fiction, the hobbits' deception only matters one time IIRC (pretending to be goblins in Mordor) and sleight-of-hand never matters--and if we're not adhering to the fiction, you're being somewhat inconsistent about your standards. Also, Aragorn does not have +8 to +9 in his best skills. He has +9 to +10, depending on whether he went for capped stats or just 18s. For Gandalf, it's +10 to +11, same deal. Covering all of Aragorn's "best skills" is probably impossible unless we allow Ranger spells to substitute for some stuff he does (the herbal healing thing, frex)--but he's a leader of men as well as an expert tracker, so I'd say Persuasion, Stealth, and Nature myself; and since he's a Ranger (in fact, almost certainly the, or at least an,
inspiration for D&D rangers) I'd expect him to be high-Dex rather than high-Str. (Nevermind the fact that he uses a two-handed sword once Narsil is reforged!

)
This being D&D, of course, the hobbits will not stay level 2 for long. By the time they get through Helm's Deep they're probably level 6, and able to survive, contribute, and even thrive in combat. 2 6th level fighter hobbits slinging stones have, in D&D, a combat profile similar to a 14th level fighter. More DPR, less HP. In the fiction it doesn't work that way of course.
That they will level up wasn't the point. Something that is actually a challenge to Aragorn and Gandalf *when they set out* will be lethally dangerous to the hobbits in combat, and skill checks that would challenge them will be difficult or (potentially) impossible for the hobbits. The only difference is that, where the hobbits are specialized, they actually stand some chance of success (DC 20 with a +5 bonus ~ 30% success vs. Aragorn's 55% or Gandalf's 60%)--but that may or may not be true for other games anyway. Areas where they're weak are still, as in every edition, completely impossible (DC 20 with a -1 = 0% success), and any given task that is initially impossible will (almost) never
become possible because 5e favors Ad/Dis rather than numeric bonuses. (As opposed to 4e, where the half-level bonus means a particular task might be impossible at level 1, hard at level 11, and between easy and moderate at level 21, as the character gains +11 to
all ability checks, 10 from half-level, +1 from the "all stats increase by 1" for each new tier.)
BTW your combat math on the hobbits is off. Even at level 1, for them to be in the "10 to 15% range" requires AC 23, which is vanishingly rare in the MM, not exactly "many" foes.
Fair. I don't own an MM. That said? AC 21 or AC 20 is not particularly uncommon, as I understand it (just plate+shield or sufficiently high dex+natural/light armor), and that's only 10 percentage points easier to hit (20 to 25% range). I'd go into how Gandalf and Aragorn are doing 3-4 times as much damage (hitting 2-2.75x as often, rolling 2x as many attacks, offset by hobbits having a higher fraction of successful hits that are crits), but you've already excused the hobbits from having to take any risks in combats that would challenge Gandalf and Aragorn.