I don't think the reaction of order schools to remain open is anything whatsoever to do with schools per se.
It's mainly about keeping central control of policy and the actions that follow from it. Assuming they see this as a thin end of the wedge situation, when they know they will be facing tough regional negotiations over new year restrictions, and might have to order compliance.
They have, blazingly clearly, got it wrong about this. No-one is suggesting that pupils in Wales have just had their futures wrecked, or that their parents have been unable to cope en masse. No one should be saying that English parents are less able to cope than their Welsh counterparts,
There is no good argument against schools switching to online (with key and vulnerable provision) in the last week of term. And indeed positive advantages if they do - 10 days of sharply reduced school-based mixing running exactly to the start of the permitted Christmas bubble days.
I would be very interested to see what happens if this does end up before a court. Though as pp said, it might all turn on arid points such as the exact strength of PHE advice (I wonder whether a written version of it exists?)