Well, greek myths are notoriously tragic. If you think about it, Hermes task is that of retrieving the source of what created the labyrinth, so there's a risk that without it, the hotel might cease to be due to how unstabble this realm becomes. Another idea is that freeing Asterion from his sentence means that he will immedietaly have to go back to the realm of Hades. Afterall, he is already dead. Hermes said that the initial plan was to give them about 20 years or something before proposing his request, so it stands to reason there would be some motive to want to stall from making Asterion free right away.
As the master of the hotel, MC already has a lot of power, and he has a bunch of mythicals to help with this task. So, I don't think there would be any reason to reward him a demigod status and even then, that could conflict with his ability to be the master, since it must be a male human (this reminds me of that non-binary mod. if this rule gives vital implications down the line, then it would make that mod incompatible with the lore). Then there is the idea that ichor, the blood of gods, is nocive to normal mortals. Even if he does indeed become a demigod, he still couldn't be made immortal, so it'd be no more than just a title.
So, right now, I see 2 possible outcomes: You don't do the task, Asterion becomes eternally bound to the realm and eventually turns into stone, or you do the task and the hotel ceases to be with Asterion being returned to Hades.