Apologies for taking so long to answer this ask (or any for that matter)

Life is kind of kicking me in the ass rn, not to mention the mental health

But I'm glad you liked my take! While in general I feel a lot of fans toss familial dynamics/relationships onto characters just cause (usually related to shipping), there are times where I do agree that certain characters are being written in such a way for the reader to be able to draw parallels to family dynamics (one example in this case being how Team Chaotix is written in IDW).

But often, even when I agree that you can read into parallels to family dynamics or when I agree with other fans that certain characters may be interesting in a familial context (another personal example for me is the idea of Agent Stone being a parent figure to Movie!Shadow), I often find myself at odds with most fans because of exactly what you described

I'm not very fond of flattening their dynamic into purely having only 'familial' roles

I get that it's easier for people to shove character dynamics into more palatable boxes. It's kind of why fandomization of characters happens so swiftly. A lot of people want to brainrot over the characters and their relationships, and it's easier to mass produce stuff for it (memes, art, fic, rambling posts, etc) if you can use common templates or tropes to do that.

But I like complex relationships and character dynamics.

Sure, I do personally read into IDW Sonic and the Official Sonic Cookbook as having an angle you can read into where Vector and Espio are the typical married couple and Charmy is their adoptive kid, but that's not all that's there. Vector is Charmy and Espio's boss. Vector has a textual crush on Vanilla. Charmy's response to Vector telling him what to do is "you're not the boss of me", before Vector reminds him that he very much is his work boss (from Idw Sonic #77). It's got this entire vibe where, well. The three live together and have been working together for a while. Their current relationship is just something that came about from being around each other and being together for so long. And their relationship and all its angles is colored by that closeness, the fact that they live together, the ages of the characters, and even the fact that their group relationship isn't solidly anything aside from coworkers.

By flattening their relationship into a cookie cutter mold for the ideal or average American family (whether you ship Vespio or see Vector as group dad), you've thrown out everything else that isn't that. And...there's no interest in that kind of relationship for me.

As a final note too, I also hate it from an analysis or "this is the characters' canon relationship basically" standpoint. Because, as mentioned, familial dynamics isn't all you can read into Team Chaotix. Their relationship is made up by a multitude of angles one can tackle in order to understand their group dynamic better. When people look at the characters and say "well Vector is basically their dad and that's that" (exploring only the familial angle), they end up ignoring any facets of the group dynamic that don't fit. If Vector is such a good dad of all time, then why is Charmy allowed on dangerous missions if he's supposed to be just his young kid? If Vector and Espio's relationship is about a single dad raising his teenage son and wingmanning his relationships, why do the two bicker about who was supposed to pay the power bill or the things they keep telling each other to stop doing?