I love that we're talking about this at all, makes for a healthier relationship than your normal VN where the MC is not just playing boyfriend but also playing therapist the whole time. Feels right in place with the effort of the MC to deal with the power difference so we can have a relationship with Asterion.
Mmm, the logic about it being a mythical is sound, especially if you want to use this character to dive into magic or if they have magic powers that could be helpful here - specifically, we already have the Tapir God and tapir are tied to eating dreams/nightmares, so a tapir therapist could make a lot of sense, perhaps? We know there's more Hinterlands content coming, if there's a tapir character there (Matias, the book author, is hinted to be one I think) they could be related to the therapist as some story beats.
But I will say that I also appreciate the idea that a 'normal' human could handle these issues, too. Sort of a 'therapy doesn't need mythical people or magic to be helpful' message. And the idea of it being a human tickles me a bit, haha, contrasting that they have to adjust to the mythicals existing and weird things they do/can do, but at the end of the day trauma is trauma and they're in their element helping these people through it, no matter what they look like - they don't need an extraordinary background to help people, even Asterion and all the crap he's had to deal with.
If you didn't want to just do a human though, you could go for a Baymax style character from Big Hero 6: some sort of robotic helper/AI that was designed for physical therapy but has become some-what sentient and wants to do mental health, and moves into an upgraded clinic after an R&D project. Then there can be a chain of projects to improve it that make more sense as R&D compared to like, needing to make 'better and better offices' for them as the project(s).
Even with that robot idea though, I agree with Foeg_lug on the placement of the content, the right way to have it is probably just having it be a base thing that gets kicked off in the main story so it's always something that's going on and can be referenced in conversations, but the MC can spend time during the day sitting in as support for Asterion during some harder sessions. This way it's not that Asterion won't get help if you don't schedule it, but that you can experience some of that story - people love supporting the moo so I'm sure they will - and maybe the end result of the chain can just be something simple like improving one of Asterion's stats by 1 and a crete themed outfit. It's not super flashy, but that's kinda the point, you're not magically solving all of his problems, just there to show support for some sessions and he pays you back with something kinda personal from his past that he made for you.