Haha, so true. I've been saying this since the game came out pretty much- I never understood the narrative of Basil being obsessively attached. In many ways, he is just as avoidant as Sunny appears to be (outwardly, at least), in several aspects of his life. For the undisclosed amount of time Polly has been a figure in his living space, he has refrained from demonstrating any attachment to her or sharing anything about himself, he has not evidently pursued his relationship with Aubrey (aided by obvious reasons), and he didn't seem too motivated to reach out to Kel or Hero at school post-incident.
And when Sunny does come back to Faraway, he mainly focuses on putting things to rest according to whatever his internal logic is- avoiding hanging out with Kel and Sunny more than he has to, and passing on his photo album to Sunny in what possibly seemed like an act of suicidal relinquishing of valuable possessions, given the state of the neutral ending. Only in the state of two active meltdowns does Basil actually beg for Sunny's presence- which could be attributed to the possibility of him just wanting *anyone* to comfort him in those moments, who knows? By and large, though, Basil seems nervous to have Sunny back in his life, and I wouldn't be surprised if he isolates himself from others more than cling to them out of fear of feeling like some sort of bad-luck charm/plague in the lives of his loved ones, given his history.
And the breakdowns were intense scenes, I get it. They leave an impression on the audience, especially considering Basil doesn't have much going for him when it comes to canon screen time. But they really do pale in comparison to the fact that Sunny's ENTIRE Headspace adventure is tied around "Find Basil, find Basil, look at all of this reoccuring visual imagery that is tied specifically to Basil, look at all of these beautiful and horrific things that are referring to Basil, look at how Headspace and characters in Headspace repeatedly reference Basil's almost unrealistically idealized traits." It's normalized and oversaturated to such a degree that I wonder if maybe it became like white noise to a lot of players? ¯\_(ツ)_/¯
And I don't mean to assume this post was meant from a Sunnflower perspective, it's just the perspective I have when writing this response- but I am in complete agreement with you regardless. I've mentioned repeatedly in past posts of mine how while Basil's attitude towards Sunny is often within the thralls of serious anxiety, Sunny's perspective towards Basil has always been that of intense longing (i.e. the entire referenced Headspace loop Sunny has kept up for four years that centers around trying to find Basil, "red string of fate" Branch Coral comment, the bookshelf cutscene in the Lost Library, "Let's make new memories together" and the hug- immediately followed by Sunny's entire house being refurnished, complete with features such as mentions of Basil working together with Hero to set up stools to listen to Sunny and Mari practice their instruments + the ever-famous "This is the chair I always sit in, and this [chair right across from it in a private, tucked-away corner] is the chair Basil always sits in.")
Given all of the above in which Sunny's complicated feelings about Basil haunt the narrative more than Basil's actual presence, it is utter inanity that it ever became a common perception among fandom that, somehow, Basil is the "icky" obsessive one- only beat out in stupidity by the idea of Sunny straightforwardly avoiding/being grossed out by/hating Basil.