The Survival roll is to choose a location where a suitably-colored dome (e.g. black or dark brown) would be difficult to spot. This only applies in places where such a location exists and you have some freedom to choose your campsite; if you absolutely HAVE to put your dome on the hobgoblins' front doorstep, there's no roll and no chance of hiding your dome from them. Ditto if it's in narrow stone tunnels with no branchings. But if you're sleeping in the woods, there's a good chance you can find a good spot; but the hut is big enough that I'm not going to give you a DC over 12, because there is no way to conceal such a large, regularly-shaped object terribly well. Thus, the DC is min(12, Survival roll). But note that enemies relying on Darkvision will have disadvantage on their Perception checks, so you may be able to get away with it.
Note that a party who was sleeping in bedrolls under the trees could make the same Survival roll to choose a good spot and camouflage themselves with foliage, etc., and would not be subject to the maximum of 12 on their DC. However, they wouldn't be as comfortable as a party sleeping in a Leomund's Tiny Hut. The hut is essentially providing warmth and comfort which, as you point out, the PCs could create for themselves via nonmagical means via foraging, at a cost in time and stealth.
RE: "would you let someone Help that check"? Yes. Someone else can choose the spot and tell the wizard where to put it. Would I let that raise the result above 12? No, probably not, not unless they have a very clever plan to disguise it as something specific which is both dome-shaped and innocuous. E.g. if they're in a place where lots of dome-shaped burial mounds from past civilizations exist, then sure, you can build a ghillie suit for your Leomund's Tiny Hut; otherwise no, that's not a thing.
The only real question I'll ask here about your procedure in 5e is:
"Why the minimum...and why 12?"
It isn't so much that I disagree with 12, I'm just curious about the reasoning behind your machinery. In 5e we have:
1) Disadvantage doing the heavy lifting (mechanically and within the fiction) when determining adverse circumstances should apply and, consequently, the action resolution will typically orbit nearer the floor rather than the ceiling of potential results.
2) We have the brutally (AS below 10) clumsy (Dex), the aloof (Wis), and the feeble (Str) still capable of pulling of feats of agility, discernment, and raw power by proxy of the inherent swinginess of the d20 roll (especially with Advantage). The large plodding Ogre (-1 Initiative) can get the jump on the quickest, most aware/(p)lucky halfling (20 Dex and Alert Feat). And that is just a tiny sample.
In light of (1) and the rife examples of (2), I'm curious why LTH engaging with the resolution mechanics (eg just straight Disadvantage Wisdom/Survival) in the same orthodox way is problematic. Given what I know about your aesthetic preferences for process sim, I have to assume this is what is governing your ruling. But, if so, why is this one a bridge too far?
Or perhaps you impose a minimum to rein in the impact of the d20 and its ability to create such jarring events?
(2) Potential rules error: there's no adaptive camouflage. It's just a color. It's increasingly difficult for me to tell whether you actually apply this adaptive camouflage idea to your AD&D games, or to your 5E games, or what. As I said above, if it's not a rules error it's merely an opinion on the value of shelter and comfort; either way it's apparently not a deliberate house rule. Agree/disagree?
(3) I presume you wouldn't prevent PCs from acquiring those better odds on the random encounters table through mundane camouflage, since people are easier to disguise than a largish building. As such, it seems to me that the hut isn't preventing combat at all. It's just giving you more comfort. Do I presume wrong? Would you refuse to let someone who wasn't using a Leomund's Tiny Hut hide themselves from monsters? If so, then we are back to the "maybe it does supply adaptive camouflage in manbearcat's game", which I would view as a rules error. But I'm presuming, currently, that you would not rule that way. It's hard for me to tell.
You've smuggled in "adaptive" here (or perhaps I haven't been clear...but I don't hold the ability to color LTH as adaptive camouflage). There is just (a) a structure and (b) the ability to color it whatever color you wish. In the case of D&D wilderness survival, that would mean a color suitable to blend into the backdrop of whatever environment you're sheltering in.
I definitely think that we have a disagreement on the value of shelter and comfort in AD&D. I'm not sure about the case in 5e. I'm going to try to have one more run at this.
So let's take a Fighter and the level 8 MU with LTH. They're travelling through that swamp we discussed (looking for a shaman, or a lost ruin or something). Its Spring so its brutally humid and constantly raining...but 50 % chance to locate Natural Shelter (rather than 40 %). They spend 3 turns looking for a suitable location/means to construct a shelter for the evening. 50 % chance to fail and have to spend a further 3 turns doing the same. That would mean a full hour invested. I don't rule that as strenuous activity (for Fatigue), but the conditions (heavy armor and gear leading to "Unprotected" status in such an environment plus the environmental impacts) would definitely mean that the Fighter would be dealing with exertion, meaning the Temperature Track mechanics and the fallout of Temperature effects and exposure such as heat exhaustion or possibly stroke. You're talking pushing on and Con checks (putting you at risk) or a considerable number of turns having to rest and the removal of armor to get back down to a normal temperature range (and not suffer debuffs to Str, Dex, Con, Land Move, Attack Rolls and possibly HP damage).
So now they've found their shelter and who knows how many turns they've spent searching and resting (could be 3...could be 6...could be 10 or more). Now they do have to exert themselves with the harvesting materials and assembly. You're talking 1d6 +2 (-2 for the helper) turns of exertion to harvest (so 4ish). Then you're talking 6 -1 (for the helper) for assembly, so 5. So 9 more turns (this time of exertion so facing the Fatigue resolution mechanics or resting 2 turns after each 4).
Those are a lot of exploration turns (somewhere between 12 to possibly 19 or more) for stock encounters to manifest.
That is a lot of duress on the characters (facing exposure and fatigue and the mechanical fallout).
That is a lot of time lost (if that is relevant).
That is a lot of time toward the random encounter clock. If you're using the default 1 per 4 hours, you're checking for them somewhere in there. If this wilderness area has an elevated random encounter clock, you might be checking twice.
So that is my case.
LTH saves you from all of that. It saves you from the threat of exposure/fatigue debuffs. It doesn't leave you vulnerable to a stock area encounter while you search/construct shelter. It doesn't exacerbate your journey's interfacing with the random encounter clock due to excess time spent on sheltering. If it does nothing else (eg if you don't let the shelter influence the random encounter die or the encounter table results), it mitigates your vulnerability and your encounter:exploration per turn ratio because of this.
Then, of course, it 100 % protects you from exposure while you're in there and it allows you to keep watch in safety. If you do have to deal with a random encounter, you're almost surely to get the drop on it. And those enemies have a -4 to attack you while you're in the LTH and they're outside.
Now...all that being said, if a group just hand-waves wilderness exploration in AD&D and doesn't use its granular mechanics, then I suspect LTH likely doesn't have much value for them. My games featured it along with heavy armor Fighters. Accordingly, it was (and is when I still run it) an invaluable tool.
In 5e, the spell is just flatly considerably more powerful.
If you don't want to have it interface with the default 18-20 random encounter results on 5e's d20 random encounter die, you've got your resolution mechanics for camo (Arcana or Survival with a Survival Help) vs detection (Perception).
Its a Ritual so no spell loadout implications (with spellcasters that have more prolific spell loadout and recovery).
You've got a defensible fortress. It blocks ethereal travel as always, but it also prevents your enemies from coming in. The bad guys can't cast spells into it. You can fire artillery out of it and you're going to have Advantage in doing so.
Going to be my last post on the subject because I think we've worn this out and I want to involve myself in a few other threads. Thanks for the conversation!