Going back a step, I think it is not always that schools 'did nothing', it was that schools didn't 'do quite what a parent thought they should be doing'.
As a primary, we had work up and running from the Monday after schools closed, and from Easter a pretty much fully-functioning curriculum - 5x each of Maths and English lessons per week, Guided Reading, spelling, grammar, a weekly Science lesson, 2 lessons-worth of History / Geography, plus PE, Art etc. We maintained a safe social media page for each class, and marked and returned everything.
This was in addition to Keyworkers' / Vulnerable childcare and, after June 1st, every member of staff who wasn't shielding being in school at least 4 days a week with returned year groups, with the remaining day spent in video calls to children at home.
HOWEVER we did still have vocal parents complaining that we were doing NOTHING, because we provided the whole thing asynchronously (not live) via a number of online platforms. What those parents wanted was full time, live lessons into which they could plug their children for the entire school day. We couldn't, and didn't, provide that - too many families sharing devices with other siblings and / or wfh parents, many and then all staff working in school.
There are still parents who claim that the staff of my school did nothing during lockdown, and were clearly furloughed - because what we provided wasn't what they wanted. We were unable to shift what we did into the model they required, because it might have met the needs of a tiny minority but would simultaneously have failed the majority (I had almost full participation from every member of my class throughout, after an initial struggle with technology and engagement).