not particularly - all assets are already used in the case of residential care so in the case where your mother needed to go into a home (1/4 cases) she'd lose the house anyway (if no other assets present) and be liable for costs down to her last 23k rather than last 100k
in the case of non-residential care currently we've currently got discrimination based on asset allocation - why should someone with a 250k home be better protected than someone who also had a similar home but downsized to a 100k bungalow and now has 150k in cash/investments?
the idea of paying for care through general taxation seems unfair to me - in some cases families will look after elderly relatives and therefore not burden the state with these costs, not to mention that plenty of the working people you'd be taxing in order to fund this aren't able to afford a home themselves yet they're supposed to subsidise the care of asset rich people with greater wealth than themselves
The idea of taxation isn't - and has never been - that everyone must always "get what you pay for".
A millionaire paying £50k tax can't demand £50k's worth of services in return. That's just not how tax works.
Let's look at your argument from a different angle... should the rich pay *less* tax because they use less state-provided services? Assuming they use private healthcare, have no need of any benefits, will not use state care in old age... etc, etc. Does that mean they should pay less tax than a poor family who will have housing support, state-provided care, use the NHS.... Because if they don't, it's "unfair" using your stated principles here.
The idea of "personal responsibility" from the Tories is just another way of saying "you're on your own". They want tax breaks for the well off, they want working families to have to pay for their own social care, health care (soon enough), you name it. And if you can't afford it, a Tory idealised state wouldn't help you out in the slightest.
Taxation represents the idea that we all help each other. Society is a collective, not a mass brawl of individuals trying to climb over each other to the top.
And that's what this election represents. A socialist, collective society or everybody for themselves. At least we have something to choose between.