The biggest issue with schools is that they are social hubs able to spread the virus through society, particularly at primary where parents deliver children to the school gates.
Normally, the vast majority of my social interactions are through my children; school (inc volunteering) and their social activities (more volunteering). There will be many parents shielding or more vulnerable. Maybe schools will be more encouraging of children travelling independently (if roads are quieter, that will help)
Schools and childcare are essential parts of increasing the active workforce (and their productivity) This was recognised with the key workers provision being made avaliable. Teachers still having to go into school makes it easier for the profession to return to something closer to normal.
You can reduce numbers in school with phased timetabling and split classes, but it's not viable to keep social distancing of individuals, just reduce group size for mixing. Reduced numbers would help with reduced staffing from shielding.
What you don't want is a perception that schools go back, things are normal and that undermines other social controls and distancing measures.
The government has been clear about infection rates, and aiming to prevent them from rising exponentially again. Schools returning has to fit with that, both directly and indirectly.
As a parent with two children, one with high functioning SNs, my priority is stability. Is it ideal for them to be home educationally? Not really, we are muddling by. The one with SNs is probably happier for adjusting to being home now. He was certainly very anxious through March. What he needs is a predictable pattern of whatever balance of home/ school. What he doesn't need is short notice instability with frequent inpredictable changes. Some children will be much better off in school (and most socially vulnerable children eligible have not been in school) but again, they need stability.
Schools are important, but they need to be planned in as part of the bigger picture.