I think that there should be a way at the end of this story for MC to either give up their power as owner to Asterion, or have a way to limit their own ability to use that power/share it directly with Asterion where it requires them both to agree to a task for it to take effect.
I have a few reasons for this...
1) Asterion deserves to be in control of the labyrinth. Not only as recompense for everything he has undergone, but also because he has such a pure soul. I can't ever see Asterion using that power for anything other than the good of others, because he knows personally what it is like to be abused by that same power. This leads me to...
2) Power corrupts... I know that personally if I were in that situation as MC it would be incredibly hard not to use that power for selfish gain. Sure at first it would be little things, but I would imagine that without someone else (perhaps Asterion) to help moderate MC's use of that power they could end up abusing that power. Unfortunately humanity has a tendency to twist and warp things towards evil, even as we try our hardest to do and be good.
3) Finally it simply makes the most sense within the (currently established) plot of the story for MC to either want to give Asterion the power to run the hotel, or to share that power together.
The primary story of Minotaur Hotel seems to be one of redemption/healing and the acceptance of 'otherness' (the literal acceptance of a mythical Minotaur as a metaphor for a person's acceptance of their own or another's homosexuality) and the healing that can then begin once that acceptance is reached. The story of Minotaur Hotel isn't about the magical powers that MC can gain from the labyrinth, that power only serves to move the plot forward or highlight how acceptance is reached within the story.
In the 'primary universe' where MC works to rebuild the hotel into something for both Asterion and themselves, it would make the most sense that at the end of that journey to either share that power between MC and Asterion (preventing the power corrupts issue by having another person to help moderate the use of said power) OR to provide Asterion with the ability to take full control of the labyrinth magic once he is free (reached acceptance of himself).
TLDR: Asterion deserves to run the labyrinth/hotel, power corrupts, it makes sense with the plot of the story.
So how does everyone feel about that? Would you want to see MC give up their power to Asterion, or even share that power somehow? What ways do you think they could go about that?
All ideas welcome! :P
[Edits for grammar]