Thing is we talk about childcare for essential workers and assume that just means medical people. But we still need people to man the power stations, to deliver essentials , to work in supermarkets, food processing factories and petrol stations etc. That's a lot of people. Many households will have such a worker
In a wartime situation (which this is), if schools or childcare are kept going for 'essential workers', whoever sets that up will specify who they are. The idea that it isn't just doctors and nurses will almost certainly occur to the government.
Why do schools have to stay fully open to everyone because there's a subset who need the childcare for essential work? It doesn't make anyone safer, in fact it makes people less safe by having much higher numbers of kids mixing, half of whom could perfectly well be at home.