There are three basic solutions mentioned here.  The first is throwing "things"to completely bury the hut and moving on.  Second is dispel magic. Thirdly is a variation of "Mario the princess is in another castle"
Right out of the gate is the fact that all three flatly ignore the fact that players/pcs can see out and the opponents can not see in.  As a result they all depend on the players not using the toxically adversarial rest rules to set a watch at zero cost to all but the smallest of pwrties -OR- Worse is the idea that they depend on they depend on players noticing they are discovered but choose to do nothing.  All good f those are serious enough problems for the scenarios that follow for serious problems of credibility in the hypothetical scenario right from the start.  While I have seen players react to being discovered during a rest i 5e by continuing their rest
, the results were god awful and players were outraged even without tiny hut.  Once you clear that gate is the problem 5e uniquely introduced with malicious compliance in the shift away from ADEU to attrition based adventuring days with the introduction short rest classes. Those PC's only need to be uninterrupted for one hour in order to regain enough nova capability to obliterate any  wanderers who discovers their rest when backed by other changes undermining the attrition over adventuring day model like unlimited at will cantrips.  The short rest PC's can go full nova on whoever discovered their rest because it's so easy to recover from it anyways.
		
 
		
	 
If the bad guys see a hut they don't need to see what's inside. In most cases the characters have already caused disruption and had other fights, the enemy is likely already in high alert.  If they weren't in a hostile environment there is little reason to cast the spell.  If a glowing dome suddenly shows up in someone's foyer, they're going to assume it's something hostile, especially when they already know someone has broken in.
If you have a lot of characters with short rest classes that just means the GM has to adjust.  In today's game I had 2 out of 5 of the party members unconscious with most of the rest in low double digits in two different combats.  The first was after a short rest (they're level 8, the monk reset most things, the barbarian got back a rage, the wizard got back spells). In the next fight after a long rest and only fight of the day it was similar, just different characters.  Probably the only reason I didn't have any deaths is because they've all purchased periapts of wound closure.  The game is as challenging as the GM wants to make it.
	
		
	
	
		
		
			I don't know if you've ever tried to dig a hole of any size, maybe even level out a few cubic feet of your yard, but it's long backbreaking work that very much would be discovered before players are at any risk of being entombed unless monsters have 
iceman style powers.
		
 
		
	 
There are several monsters that have burrow speeds or can phase through solid rock.
	
		
	
	
		
		
			I'm not aware of many monsters competing with Bobby Drake on that front, so we move on because that first example is one that depends on questionably believable players who choose not to react and nakedly adversarial fiat empowered foes.  That beings it to the dual rest/recovery cycle.   Yes, eight hours is a long time where monsters could accomplish a lot , but the party doesn't need 8 hours, they need one. The volume of patrols and wandering monsters needed to thwart that shifts from d&d to half minute hero eal quickly without video game style unlimited monster spawns fueling it or something.
		
		
	 
I have no idea what you're talking about, sorry.  They took a short rest in today's game by casting Prayer of Healing which gives them the benefit of a short rest.  Didn't help much.
	
		
	
	
		
		
			On the cast dispel via slot/scroll front you immediately crash into the massive world building implications of what having dispel magic that common triggers. I'm not even going to thought experiment what that nightmare realm might look like but the closest I can imagine would probably look a lot like the world of Peter V Brett's demon cycle where relatively mindless monsters spawn and try to kill anything living every day after sundown... Roger half grip may have been the best example of abats I've seen in fiction,but I can't imagine running or playing d&d in such a world
		
		
	 
I regularly give spellcasters spells they don't have on their prep list - I view those as a quick guide to what they're probably going to cast. Besides my example was going to get someone else (perhaps involuntarily) to cast the spell.
	
		
	
	
		
		
			All of your solutions pretty much dependon the players not being willing to do the thing they are so heavily incentivized to do by the system design and all of them quickly encourage the players to take on a more adversarial players vrs gm mindset where they view thegn as an opponent to win against.  That's a toxic mindset that does horrible things for the longevity of a campaign.
		
		
	 
Again, not sure what you're trying to say.
	
		
	
	
		
		
			Finally is the monsters leave with the mwcguffin. Great quickly one of two things is going to happen.  Either your world descends into a crap sack world akin to golarian's darkest timeline where all APs failed in the worst possible way or the players notice it doesn't matter anyways.  Those two are obviously new problems of their own and still have not solved the initial problems tiny hut  caused
		
		
	 
What does one have to do with the other?  If the enemy knows they're being invaded and reasonably believe they cannot defend against the invaders the logical choice is to leave.  Sometimes that means they take whatever the characters want with them - why wouldn't they? Don't want that to happen? Don't rest for 8 hours just because it's convenient.
	
		
	
	
		
		
			I think that the only things you've shown is that your players have never pulled the  campaign on the sacrificial alter in ways that made you take a good hard look at the spell while daring you to stop them .  Adversary creatures acting intelligently is not the problem.  The results of invoking so much fiat and overtly drawing on litrpg dungeon core style powers required for they intelligent reaction to matter given the stratospherically high bar set by tiny hut and 5e'sbdusl track overly generous rest/recovery mechanics is why tiny hut unreasonably creates problems.
		
		
	 
I'm just relating what I've seen and done.  Casting tiny hut in no way guarantees safety or lack of action on part of the enemy if the hut is detected.  If the hut goes undetected then they likely didn't need the hut in the first place.  As I said before, unlike a video game the antagonists respond in a fashion I find logical given what they know.  There is no one automatic response, I just gave a few examples of what might happen which ... as expected you nit-pick with no real counter other than telling me I'm GMing wrong.