Talk to the school and try to keep them enrolled, maybe with a reduced timetable as Plan A. I wonder if your DC would agree a compromise like doing one or two subjects in college and the rest from home with a tutor. School will be used to students being EBSA and are unlikely to chuck an A grade student out early doors if they keep handing in whatever they need to. NEAs, curriculum coverage and exams will be so much easier with current school. I'd suggest keeping the reasons to MH in discussions with school rather than the quality of the teaching.
Also going into college regularly, even for just one subject, would make it easier for your child to attend for the actual exams. This might make sense to them as a reason to keep going in. Maybe also, if MH allows, raise the idea that tolerating a lesson you are not loving, taking what you can from it, is a study skill they will need for uni. Some lecturers will be poor, some units will be compulsory and not their cup of tea. Keeping "in the room" will be important at undergrad level.
At this age they can be very black and white and plump straight for one solution as the only possible one. Other ideas include dropping out for this year, working on recovery and rejoining in Sept (6th forms should all allow a 3rd year for this reason) or asking for adjustments to homework load. Also I would try to plant the idea that 2 runs at Y13 is completely fine, whether that means staying in school this year and doing own retakes next year if needed, or trying it on their own this year and retaking with a taught Y13 (online school?) next year if needed.
I have some sympathy for your child. We get a similar moan from DD that with all the pre-learning she has to do, actually going to the lessons feels like the least valuable part of her week. But she knows herself, that she only does the learning because of the structure and work set by her teacher. On a bad day she frames it that the lessons are the "price" she pays for that structure, which she absolutely relies on. Going it alone might be a sensible plan for some students, but it won't be right for everyone. You know your child best - would they plough through the curriculum independently or procrastinate and get depressed? I think these particular subjects are some of the hardest to do with no teaching, and the hardest to be confident that an A grade in class will translate into an A grade on exam day.
I would look to maybe meet DC half way and try to agree a reduced timetable with school that still keeps them on track to sit their exams there. (Also is this PowerPoint etc a distraction when they should be doing their NEA?! DD's Eng is already handed in and Hist is due in next week!)