There is actually a pretty large pool of supply teachers who would love the chance to help. Schools are quite rightly wary of engaging supply, who wants someone who's already been to for different schools that week? But if supply teachers could be allocated a single school, act as floating support within the school when there is a full compliment of permanent teachers then step up when needed during absences that would be more manageable.
Sadly, supply rates are so appalling (frequently less than M1, sometimes as low as £50/day) that the govt would need to step up and throw some money at the situation.
There's so little recognition and understanding of the position teachers are in and the stress they are having to function under. People were quick to understand the situation in the NHS but even after months of homeschooling there is still a serious lack of understanding from both parents and govt of the situation in schools now.