Both the school I work in and the school my younger two DC attend have spelled out right from the start that parents should only request key worker spaces if they can absolutely not take care of DC at home.
They could not have spelled it out more sensibly and articulately. The message has been clear: please only take up these places if you have no other option.
Problem is, parents hear: I'm technically entitled to something so I'm gonna take it!
Human nature is fundamentally selfish, and our instinct will always be to take care of ourselves and our nearest and dearest rather than 'doing the right thing' for the country as a whole.
I'm a keyworker (school office worker, will need to be in five days a week throughout lockdown, albeit PT hours). In theory I could have requested a space for DC (Y6 and Y3). We haven't, because DH is working from home and we don't feel we can justify it - I can supervise the home learning as I work PT and then they'll -have far too much bloody screen time- be taken care of by DH whilst I work.
But God, the number of friends who've expressed absolute disbelief and amazement that I haven't 'taken what I'm eligible for' is quite an eye opener. Never mind that we don't actually need it. Most of our friends think we're mad. Most of my friends who are in a similar situation (one PT keyworker, one parent WFH) have taken up their keyworker spaces like a shot BECAUSE THEY CAN AND IT WILL MAKE THEIR LIVES EASIER.
This is the fundamental problem, we're all conditioned to put ourselves and our individual families first (aka taking the piss, in many circumstances), and this is why so many parents are not looking at the wider picture. And this is why there are so many kids in school.