No it dosn't. The state pension isn't a state benefit and neither is the NHS. 
So, just to be clear then, if I and my identical twin brother arrive at age 70 and retire. With £500k in the bank each, then I get a brain tumour and he gets dementia.
My treatment (chemo, numerous surgeries, nursing care etc) costs the state £100k. His care, in a home costs also £100k. Then we both die. In your world view, the £100k spent on my care is fine. But my twin brother needs to pay £100k for his care.
Thank goodness it's not an arbitrary distinction based wholly on chance.
Also, why isn't the state pension a benefit? I suspect mostly because it gets the olds' backs up.
Okay, say unfortunately, you and your brother both get cancer. The new wonder drug treatment and cure for your brother has been approved by NICE for the NHS to give to him FOC, your different wonder drug treatment and cure is not considered value for money by NICE, not approved and is not available on the NHS. The only hope you've got is raising the £1m treatment cost and going to the US for treatment. This is the luck of the draw and the lottery of life.
Read any decent book on economics and invariably the first sentence is along the lines that "Resouces are scarce and always limited". They are and lines have to be drawn on affordability. The problem with socialism is that everybody wants to benefit at no cost in time and money to themselves, which means it is at the cost of somebody else's time and money! In the end the people that can don't due to penal tax rates. Successful people get there through a combination of taking risks, hard work, vision to create well marketed desirable products and services, but as they only get 24 hours a day like everybody else, it is normally at the expense of working long hours. Take away the reward and they will be down the pub instead like everybody else who only wants to work 9 till 5 or less.
When I was
hatched born, I didn't get a certificate telling me life was going to be fair and I don't know anybody else that did, but maybe you're the exception?

When I had a flu jab on the 4th October 2015 there was a 1 in 1,000,000 to 2,000,000 chance of it containing a mutated life changing virus. Unfortunately, that was me and the end result is that I'm partially sighted. Now I could mope around all day, be all bitter and complain about how unfair life is or accept that sh!t happens and get on with life. I personally accept what has happened and get on with life.