any time a teacher is off can be spent with a very short stint of remote learning
Can you explain how this works?
If as a primary teacher I am ill, then my class is sent home at once until I am fit to come back in - which could be 10 days, or much longer? Who sets this home learning? Me? I am ill. My poor colleagues, who already have classes of their own?
In secondary, how would it work? If the English teacher and the history teacher are ill, do children go home for those periods? Do they sit in their normal classroom without supervision, expected to do 'home learning' on whatever device might be available?
I don't think you have thought that through. What is actually happening is that if a teacher is ill, any warm body is put in front of the class - in primary, we have had unqualified TAs, we have had receptionists, we have had lunchtime supervisors, we have had unsupervised student teachers, as we are utterly unable to afford or get supply staff. If they are lucky, some cover work has been set. If not, children are essentially given 'busywork' and child-minded. This can go on for weeks.
in secondary, equally, those subjects where a teacher is absent, a warm body - from another subject, or support staff - sits in front of the class and the class does busywork.
When the school runs out of warm bodies, it closes partially or wholly. However, education hasn't been going on for days or weeks by that time, with children developing huge gaps in their knowledge.
Of course, the government could help - making up all supply payments would be a really good start - but they won't.