If people are going to be expected to give up their homes when they find there is more space than they used to have they will wonder what the point is of buying them in the first place. On the whole, people in the UK buy houses so that they aren't paying rent into old age. A home represents security.
Yes, we need to build more houses, and we need to do something about prices so that young people can afford to buy and geographical injustices are levelled out, but the answer is not to make people feel guilty about staying in their own homes - particularly when it is still legal for people to have more than one. Stop that first, and yes, stop housing stock being sold for AirB&Bs. Maybe look at reducing the cost of moving, too. I suppose much depends on local markets, but often downsizing doesn't leave a lot after estate agents, stamp duty, conveyancing, removals, new carpets and curtains etc are taken into account.
Our house is a family house, but we are still a family, even though the children have moved out. We have four bedrooms, but need at least three (a bedroom, a spare room and a study), so downsizing isn't going to save us a lot of money, and where our house is located is ideal for older age, as it's on the flat and near all local amenities. Deliberately moving away from that would have to be very cost-effective to be a remotely attractive proposition, and it just isn't.