Dd1 knows of at least 2 families who’ve been taken in locally, in Oxford. One of those hosts is a single woman in a 3 bed house, the other has a spacious annexe.
A niece of dh with 3 children of her own has taken in a mother with 3 children, but she has an enormous house - she still has at least one spare room.
I would guess that many people simply don’t have the space. We already have a shortage of affordable, adequate accommodation in this country and a good many families with children are already in considerably smaller housing than they’d like.
Out of interest, have you offered to host, Varian?
We did offer one bedroom for a couple or mother with a small child - a king size bed but no room for another - but no bites so far, and if I’m brutally honest, it’s a relief. We have no separate living area to offer and I think I wouldn’t cope well with anyone else around almost indefinitely.
My intensely sociable dd1, OTOH, would be fine with it, but with 3 children of her own she just doesn’t have anything but limited space to offer - but she has offered that - again with no takers.