Of course it's not fair to give your money away so you can get state care! Imagine if everyone did that.
We are living longer, a fact, someone has to pay for our care should we need it, another fact. We can't expect to pass our money to our children while the younger generation pay out for our care thinking that as long as our offspring are doing ok, that's fine.
Some time back, they were talking about putting a ceiling, e.g. £72k that you could reasonably be expected to either keep or pay towards your care, I can't remember which way round it was. I think that sounds fair.
Meanwhile, we live in a house that is too big for us (not huge but definitely could make do with something smaller)and see how the younger generation have all but given up on ever having a home to call their own.
We are having our time, have had a lot of it, we had expectations that were usually more than met. We managed to save a bit, which is fine, but we really can't justify our goal being to hand on all our property/savings. I don't know about others on here but I know that my own two have made their way in life, own homes, children etc. If anything, I would consider leaving a bit to my grandchildren whose parents may well live even longer than us older people, with good healthcare etc. But I fully expect to have to pay towards my care costs/living expenses in my old age, if I am lucky to get there.
Re savings, there will always be upkeep on one's own home, even if we downsize. I think that a reasonable amount to have in savings would be approximately twice your annual pension income which, in our case, would be around £60-70k. We don't have anything near that but I think that would be comforting until we have to downsize.
But I would expect that to dwindle over the years as things need replacing.