"The house equity all those boomers have acrued will go on their care home fees, not their grandchildren."
I don't believe that's true in general, although obviously there will be cases where it is.
The average house is now worth about £160K, but there's a strong chance that older people are slewed towards the upper end of values. They will all have 100% equity. Of the pre-war and boomer generation, a lot of the home owners will have significant pensions, because they are the golden generation of defined-benefits pensions, even in manual and semi-skilled jobs. There is huge social services effort to keep people in their own homes, and people only spend quite short periods of their lives in care homes, and often it's only the surviving member of a couple who goes into care after their partner has died. Again, generalisations.
If you're a couple sat on ~£200K of asset, with a pension income of ~£15K (state pension plus small occupational pension), even at £25K/year/person four-person years of care home still leaves a substantial asset behind. And a lot of people who worked in the public sector or the large industrial sector - the two key employers of the era - will have better pensions that that: 50% and 66% pensions are not uncommon. And that's assuming the only way to fund care is to sell the house and put the money under the bed to pay the bills in cash: even in the current climate, the discount rate is not zero. And it's also assuming that the only asset is the house, which is not necessarily true.
Yes, obviously you can't say "all old people's finances look like this", and there's huge disparity. But one of the things that has driven the buy to let madness has been boomers inheriting from their parents.
It's also assuming that grand parents don't decide to fund their grandchildren's education on the assumption that means tested benefits penalise holding assets. There's some evidence that's happening, I believe.