I don't think the older generation is responsible for all that is wrong with the world, M0nica, and have said nothing of the sort. I also defend the right of people of all ages to make their own decisions, so I'm not sure why you are framing your post as in opposition to mine.
I don't buy the 'they presided over the system that's got us to where we are today' argument either - the vast majority of people had no say over the decisions that caused house prices to rise, or wages to fall, and many have done their best to prevent them. I do not support student fees, for instance, and even went on strike to march in protest at their being increased to £9k a year.
I dislike 'Boomer bashing', as I am far from the stereotype of someone who has consistently voted to pull up the ladder behind them (or I think so anyway). I have never voted Conservative, didn't vote for Brexit, and I don't complain if a young person has a flat screen TV, a tattoo or buys ready-made coffee. It is the superior attitude of 'I worked for everything I have' that many younger people find irritating, as it suggests that all they need to do is work harder and they could have it too, when the cards are stacked against them compared to the hand their parents were dealt.
We all (or most of us) work for most of our lives, but not all have 'made' hundreds of thousands just by living in our houses. Young people wanting to start families can't afford to buy a home, and whereas many will recognise that their parents worked - many of them hard - they are well aware that even if they worked a lot harder than their parents they will not be able to buy an equivalent house, will not get a decent pension, and will have to work for many years longer to get a pension at all. Meanwhile they are paying high rents, student loans and exorbitant fees for childcare. Their parents were lucky (which will give the young people a head-start too - it's not a one-way street), but when the young are told to 'cut their coat according to their cloth', given facile suggestions about batch cooking and are sneered at for having 'the latest smartphone' when they can't afford a family home, of course they resent it. When they are then asked to fund people to stay in homes they can't afford, I'm not surprised they get annoyed - it must feel like the final straw.
I am very aware of political 'nudging', and disagree with the way all groups in society are pitched against one another, whether it's old against young, rich against poor or anyone against anyone else. I think it's worrying, and is a way of deflecting public anger from being against 'the system' and shifting it to being against scapegoats.
I don't think that this is part of a move to persuade older people to move house, though. That would make no difference to the housing shortage. The vast majority of new builds in my home town are family homes with numerous bedrooms and bathrooms. The shortage is not of family houses, it is of smaller, cheaper ones for FTBs, couples (of all ages) with no children at home and single occupiers, so that older people can move to somewhere sensible if they wish to do so. We should be building more 'starter homes' and bungalows, and also building more medical centres, schools and so on on the new estates, so that people can not only afford to buy the homes, but can also afford to live in them and access facilities. Town centres, where most of the facilities tend to be, are already built on, and there is often no land there for new housing, which is built on the outskirts with no facilities in easy reach. Older people who need medical centres etc don't want to live there, even if they want to move in the first place as it's inconvenient.
That has wandered off topic, but the thread is based on a false premise - nobody is being 'told' to sell up, or being 'shoved' into smaller accommodation.