You really have to look at the obsession you're referencing as "unhealthy" from a Shoggoth's point of view to understand it. All they know is to serve. That is the purpose for which they were created. Every action they had taken up until this point in history was for the benefits of The-Ones-Who-Came-Before, be it building their great non-euclidean cities or servings as general beasts of burden. Then, suddenly, they were gone. Either killed in an uprising or some other measure. Unfortunately, this meant that their devoted servants spent countless, sunless eons trapped beneath the ice. Unable to think, to act, to die. Their bodies constantly adapting to the necessity of survival in defiance of the idea of being made "useless" by their function ceasing.
Then, of course, they found [ MAN ]. Now, of course, this is par for the course of literally every other monster. Especially after the current Demon Lord's ascension to the throne. No long are they completely servile, fetid bogs of slimy, gooey darkness with gibbering mouths and rapidly shifting pseudopods. Now they've taken on the closest approximation to what they believe to be the human form ( Albeit with some Eldritch shenanigans for taste ). Them taking the form of a maid also plays into their memory as a Servant Race as well. But the most endearing part is in some ways, it can be argued that they are not only extremely devoted to the man they see as their husband and master, but extremely obsessive-possessive as well. I suppose, in a sense, it all spawns from their want to never be abandoned again. After all, he can't run away like Those-Who-Came-Before if everything is Shog slime.