Staying at home and going to local college is not necessarily better for MH: it's an individual thing.
My dd is so much better since she left home and went to study in London- she is a completely different person! I reckon another couple of years in the town where she had been ill for so many years of adolescence might just have broken her. She needed to break away, she needed the space to breathe, she needed to believe in her own independence.
She is very clear that this is not an issue with us as a family, she gets on well with us all, she still rings for a chat whenever she is feeling low, she loves meeting up- but she cannot cope with living at home. She is even wary of coming home for the holidays for more than a few days because she knows it triggers her anxiety.
As a parent you are not always best placed to help your struggling child; I am very glad that dd has access to understanding tutors and a system in place that she might not have at a local college.
I have also spoken to students who feel their MH problems have been exacerbated by their families and who have needed to get away, even from very loving homes, for similar reasons.
If anyone had told me what my dd would be like after 2 years away, I would not have believed them- I would have cried for joy if I had (in fact, I'm feeling a little teary now).
I think one should be very cautious about trying to decide for a young adult with MH issues what exactly they can cope with or can't cope with. They need to learn to decide that for themselves.