Teachers cannot be key workers if they are able to not attend work for 18 months+.
I'm sorry to hear your specific children's school has been so poor. Are you considering moving them to a school where you can trust the school? I assume you've gone down the proper channels to discover why your children haven't received what the GOVERNMENT have told them to do so.
However, not all schools are like your experience. Infact many are providing a good, albeit distanced, education for their children. The teachers at my school have all attended school full time since March. Almost all worked in school through 3 weeks of their holidays in April and May. They have PPA time where they can work from home - this is .5-1 day a week depending on if they have management roles.
I admit that I haven't been in school during lockdowns. Due to being vulnerable I have followed the advice of my medical consultants and Gp and am fortunate to have a headteacher who cares about their staff. My school role means that I can work effectively from home - infact during periods of remote learning I am better to be home as I have better tech and better WiFi, and my role means the other staff are supported more effectively especially when in class. However, like many workers who are wfh, I am doing longer hours than ever before. There's no real distinction between home and school now and my working hours are huge. I'll be working all afternoon today. I rarely finish before 6.30-7pm week days, and work during the holidays at present.
I did go into school full time in the autumn term with no SD, no masks, nothing bar an open window. I'm CV but the government still expected me to be in full time with no protective measures. I was teaching over 200 children weekly with no SDing, I did catch covid, was in hospital and was off for 7 weeks. And I worked throughout that sickness, from home. Heck, I even answered parent queries from a hospital bed!
So yeah, don't really buy your whole teachers not working rubbish!