I think in the short term things are so out of control they have no option but to close the schools. Things feel totally different today than they were even a week ago. Countries are literally closing their borders to us and we are being warned about possible food shortages. We have got to get the R rate and case numbers down and that's the end of it.
Of course keyworker and vulnerable kids would still need to be offered places like the March lockdown. They can utilise the furlough scheme for other working parents who don't have other childcare options. I think that should include parents of primary kids who work from home. I can't even imagine the stress of trying to juggle looking after a little one and the demands of a job that people went through last lockdown.
Longer term, they need to address school safety - the mass testing is a good idea but it needs to be combined with other mitigations - this could be blended learning, temperature checks, masks, proper filtration systems, or allowing parents who are in a position to, to temporarily home educate etc.
It will definitely help to get teachers and other school staff vaccinated - obviously NHS and other care staff would need to be prioritised, but following that teachers need to be on a priority list. There's a petition here for anyone who wants to sign
petition.parliament.uk/petitions/554316
The plan to keep kids in school who are close contacts of positive cases on the basis of daily lateral flow tests needs to be binned - the tests miss about 50% of positive cases so this plan is frankly dangerous (especially if this new strain is as infectious as they are saying).