"Not the cause of majority transmission" is difficult to pin point as the stats are unpublished as far as I know. But it would stop disruption of the teachers going off sick which would help. As for the in school measures of set spaced desks, one way systems, face masks they should be in place at least until the summer holidays.
I agree no UK government has covered themselves in much glory but at the risk of scrambling for crumbs of comfort it was good to see DFM acknowledge that schools weren't virus free havens but the economic and societal damage of closing them outweighed the medical need to close them again. It would be useful to see their workings that led them to that decision.
But I completely agree with you the school's can be a switch we turn back on as soon as say the over 80s are done we need to see a gradual reintroduction of all sectors where possible i.e children in homes with parents of 1 key worker can return and children with coursework difficult to complete at home can return at the same time outdoor sports and self catering wholly contained holiday let's reopen, as an example.