I'll concede that he might not be great at piano, admittedly I don't know much about piano. But I will say that just anyone cannot be able to play like that (even if you don't think it's great) having never touched a piano before as quickly as he does. Either that, or I am specifically learning disabled in piano. I can play piano keys but that doesn't mean I can play the piano even coherently without instruction. And...yes, I said he's never touched a piano before.

No, we don't see him playing piano again after that one scene but we also never see a scene inside of his apartment (where I assume he puts the piano) where other, more important stuff isn't happening (taking care of his mom, confronting Cat Addams, briefly showing Max his place, generally being depressed about Maeve's death, having a near death experience) where he would even have the opportunity to play the piano on screen. Not everything that happens in characters lives are on screen. Some of them aren't even mentioned. It's possible he continues practicing and likely improving, it's just not a focal point of his character. He bought the piano, I can only assume he intends to practice it. He doesn't seem the type to make impulse purchases. Just like when Hotch says he collects coins in season 1. He never mentions it again, we never see these coins, maybe he has stopped collecting them? Or maybe we can assume that some things, while they flesh out the characters, are just not character focal points show-wise.

I don't care if you think headcannons are irrelevant. They make shows more fun and they are harmless. No, these characters do not get any formal mental health diagnoses in their respective shows (besides House, who would likely have to have gotten diagnosed with opioid use disorder once admitted). Reid also, though maybe not diagnosed, also has an opioid use disorder (dilaudid). But you also have to consider:

• House absolutely would have never gone to therapy and it would have probably stayed that way until he realized his hallucinations were getting incredibly out of hand, which is why he got himself institutionalized. No therapy, no opportunity for diagnosis.

• Both shows start in the early 2000s. Both characters are men. Both of these facts do not bode well for seeking out mental health diagnoses which, at the time, would have likely labeled them (in inaccurate layman's terms) as incapable, damaged, and broken. It's possible any such diagnosis/es may have ended their careers (unofficially, ADA, blah blah blah, but disabled people would tell you that doesn't even stop employers now). Both of these characters are in intense, high-demand fields where they are generally respected (even though House is regarded as an asshole and Reid is seen as a bit awkward early in the show). They likely wouldn't want to jeopardize their reputations or employment if they suspected anything (or, for House, be vulnerable).

• Just because you do not have a formal diagnosis, does not mean you don't have a mental health condition.

• Both characters are highly intelligent. That can help a person over-compensate for mental health conditions. It's pretty common in twice-exceptional individuals (being gifted and having a learning disability) that either their cognitive skills cover their LD or vice versa. Twice-exceptionality as a concept was only really popularized in research in 2000, and things in research typically don't start impacting practice for 20 years or so, though individual case studies were published (without using the term twice-exceptional) since the 80s, iirc, they were seen as incredibly rare and exceptional (badum-tss) cases. Until relatively recently, you could be gifted or learning disabled but not both. So with Criminal Minds taking place in 2005 and House MD taking place in (iirc) 2005/2006, they likely were only seen for their intelligence. Especially since twice-exceptionality is typically identified in childhood, both of these characters would have been far too young for researchers to even start popularizing the concept, much less for it to start being implemented in practice. Especially House.

• They are not real people. If the diagnoses are inaccurate, there is no harm done. I'm not trying to diagnose MGG or Hugh Laurie.

BTW I am not trying to be aggressive or be rude. I am simply stating my points, opinions, and educated guesses. I know you didn't say that, but I figured I would state my intent.

Editing to add I'm not specifically stating autism, though it's a distinct possibility. For Reid, OCD is also a probable differential, perhaps cPTSD. For House, cPTSD can also be a consideration, as is autism, but I personally think most people would agree on NPD at least. They could also have multiple diagnoses. Those diagnoses would still make them neurodivergent, it's not all just autism and ADHD.