OP, I am really sorry that your child is experiencing MH difficulties, and I know how this can affect the family.
I can only post from experience, and, like another poster said, there are a lot of other variables to consider with respect to whether home schooling would be better for a neurodiverse child with MH issues.
In my case, both my sons stopped attending school due to MH issues. One was in Y8 and one in Y10. By the time they stopped attending school, their mental health was so poor, that they could not access 'education', and had to be supported to attend therapies. They rarely could leave the house and my eldest became an inpatient in a CAMHS unit.
When they were both at home, home was a really unsafe environment for them. They both needed constant support and supervision and each boy was keenly aware of the other's anxiety. Add psychosis into the mix and serious self harming and you can imagine that there was little chance of educational activities.
Yet, comments from my eldest child's TA, in his message book, showed me that the school was dealing with my son's mental health crisis as well, and little education was taking place because he could not access the classroom, he was self harming at school and he had to be constantly supervised to prevent him from running into the road. I am keenly aware that schools often have to cope with serious MH issues in pupils. My youngest coasted in the bottom sets and finally broke at the age of 13.
In retrospect, I think both boys would have benefited from a well planned alternative or specialised provision when they were well. By the time their MH had reached the point that they could not attend school and/or were not safe in school, there was little chance that they could actually access any meaningful education.
We had to try to educate the boys at home (apart from the CAMHS admissions). It might have worked if the boys were mentally stable and perhaps a little younger. In the circumstances, we just took two dangerously unwell boys from one setting and tried to manage their behaviours at home. This was not the right decision, but it was the only choice we had.
Obviously, I am writing from my own experience, and many people have home -educated their children with really positive results. However, in our case, our sons needed much more help and support than either school or we could give them.