But if you're going to allow 20+ households to mix in classrooms 6 hours a day, 5 days a week, then I don't think it would be too much of a stretch to allow households to mix indoors with limits.
This misunderstanding is at the root of much that is wrong with people's approach to Covid - and the fact it is so prevalent is an indication of the total failure of the government's communication, right from the start.
We know that schools contribute around 0.3-0.4 to R, a measure of Covid spread. We also know that indoor mixing contributes significantly to R, though I am afraid i don't have a figure on that.
The point that the government fails to communicate clearly is that there is a choice as to how we 'spend' this rise in R, or if you prefer, this amount of risk. If the two activities are the same in terms of actual risk, the effect of doing both is additive.
So, for the sake of argument, say that schools raise R by 0.3, and so does indoor mixing in groups of a particular size. And say R is currently 0.69.
If we open schools alone, R becomes 0.99, and the pandemic continues to shrink.
If we allow indoor mixing alone, R becomes 0.99, and the pandemic continues to shrink.
However, if we allow both - even though they are exactly the same level of risk, so people say 'well if I can do X, then surely I must be able to do Y, it's no more risky' - then R rises to 1.29 and the pandemic starts growing rapidly again.
That's why the government has to make choices - it can't open 'everything that is perceived to be of the same risk', which is what many people assume, because the effects are additive.