I'm a teacher, and my school provides 3 hours of work per day. It is a difficult balance because half of the parents are clamouring for more and half are telling me they're stressed by it all. I've opted for providing it, for those that want it, and making it clear that there is no pressure to do anything.
Out of my class of 35, about half are submitting everything, and the rest submit one lesson per day. I only have one child who isn't submitting anything.
I'm really sad to hear so many are struggling to motivate their children to stay engaged. What I wanted to add was that schools do not expect you to be teachers. We know you are stressed and busy. The work should be things that your child can access independently, or a recapping of previous learning. It should require a few minutes to 'set them up ' and then they should be able to complete it largely unsupervised. If that isn't the case, I'd suggest contacting the school for advice - it may be that your child could be sent the work for the year below, for example. Certainly, the school need to hear your feedback. It might be that a call from their teacher would help with motivation.
But, unless your child is very young, I do think that no engagement with learning whatsoever for a potential six months is a bad idea for your child. It will make the eventual return so much harder. Even if you can only do some reading and maths, say one hour per day, it would pay dividends.
Teaching your child that kicking off and causing a fuss gives them what they want - no work - is not great. Work out the best time for your family - an hour first thing, four 15 minute sessions - and make screen time (or whatever they love) dependent on their best efforts.
I know how important mental health and wellbeing is, especially at this time. But doing nothing is just kicking the can down the road imo.