excuse me while i laugh for 10 minutes straight
He absolutely is willing to learn. Actually, it's been interesting watching Dan grow throughout his time at Giant Bomb, particularly since moving to New York. He's become more self-aware, less resistant to things that are foreign to him, and more graceful when it comes to expressing his quirky ideas. In general, he's seemed like a much more mature version of the guy that was originally hired, who was already pretty cool.
It's just that he hasn't become a completely different person, and still leaves plenty of room for people to judge him harshly. In this case, a series of things have happened recently (and our recency bias is pretty affecting) that are only loosely related, but have continuously added fuel to a particular narrative in this thread: his silly science questions, the highly personalized critique of Pyre that some blatantly overreacted to, the moment when he gave into his worst habits and blindly defended Walmart, and so on. Individually, only the Walmart thing actually deserved to be called out, but negativity is easily self-reinforcing, and it's easy to see the worst in everything Dan does.
When it comes to his ignorance about science, I find the criticism both understandable and unfair. I think it's good that he asks questions, and is willing to admit to how little he knows. He forces people to think about things they take for granted, and has triggered an unusual number of conversations about how the world works. The part I find unfair is where people who are normal and therefore know the Earth is affected by the sun's gravity seemingly express impatience for Dan's lack of retention. When you don't have that broader web of connections creating context for the answers to your questions, chances are you're going to have to repeat them once in awhile.
Of course, Dan's particular mix of curiosity, openness, and actual interest in doing research can definitely be frustrating, and Vinny's totally justified in asking him things like, "Okay, if I recommend you a book, will you read it?" in response to his questioning.