Claire living at home actually doesn't feel off to me, to be honest - yes, she's a driven grad student, but she's also the kind of person that wants some stability to come home to, and having a supportive family to come home to is a huge plus especially in her situation. And, there's the financial advantages, with how expensive education in the US is.
My remarks about her not having the life experience of living on her own are in regards to what it may mean if she were to move in with Marten (having known couples who have had problems with one partner moving straight from living with their parents to living with their partner, and effectively expecting their partner to take the role of their parent(s) as far as home life). Basically, fights over simple domestic stuff. (And I don't want this to be taken as "her role is to be a good housewife for Marten" - the most prominent example in my mind is a former friend whose boyfriend had moved straight from home in with her, and didn't carry his own weight and expected her to be a good housewife for him, rather than an equal partner.)
And, yes, Claire having zero relationship experience is a bigger hurdle, but even after clearing that one, the hurdle of not having lived on her own is still there.