I prefer to stop somewhere along the path and enjoy my own food in peace in nature, preferably with a nice view and without crowds, curious looks or even stupid remarks. After all, I'm on a trip in nature. I don't know why one must eat just in the hut (except of course if the weather is bad). Sitting on a stone, rock or stump hasn't bitten anyone's ass yet, plus there are benches along the path here and there.
Abroad, all mountain huts have the status of a restaurant or, if they have beds, a pension, lodging... The difference is only that this restaurant or pension lies at a higher altitude.
On one hand, this is bad for those who must eat just in the hut, because they won't tolerate you eating your own food in the hut practically nowhere abroad. A place is a place, at a few 100 or 2000 meters.
On the other hand, all restaurant rules and laws also apply to high mountain huts. There's nothing like here, doing something "home-style" (as if above 1000 m no laws apply anymore), bypassing rules and some nonsense. This concerns service, bills, taxes, consumer rights as well as behavior rules in private spaces of public character.
This also brings, on an informal level, a better relation to the customer, fewer misunderstandings because laws regulate everything, and greater satisfaction both for the keeper and for the customers.
So, for example, there it can't happen that someone stages a full picnic on the table; if it does, the owner of the place (after probably first friendly warning you) has the legal right to act, and only here can it happen that someone primitively threatens the guest with some gang of thugs and the like.
In the land without law, what happens happens... just like in areas of everyday life too.