So you're contacted at work to come collect your elderly infirm relative who you don't get along with. They can't be discharged to their own home as unsafe to be left alone at all and they're being discharged into your care if you like it or not. Do you take them to their own home and leave them there to die? Let's say you have no conscience, they die, does that make you guilty of manslaughter? Prison? Lose your job, your own family evicted, now homeless, no social housing so what now? And how to put your life back together when you're released.
Or do you take the elderly infirm relative back to your home, which is now overcrowded because you didn't have a spare room, so relative is on the sofa. Kids have nowhere to play and have to stay quiet, you're stressed trying to make it work and keep everyone happy, run ragged.
But it doesn't work because you've lost you job now you're a full time carer earning £60/wk (ish) so your family is struggling to make ends meet, no luxuries and no fun, maybe no heating. You become depressed because your relative who you don't get along with isn't even grateful and is ever more demanding. No family life you've no time, no sex life you're too knackered, partner resentful of doing all housework and childcare when they're not at work. Your family breaks up, now you're facing eviction because you can't pay the bills or work and awaiting non-existent mental health care. You lose your kids who go live with your ex because you can't house them.
Your kids are messed up for life because they were emotionally neglected, have a strained relationship with their parents now, trauma from being homeless, anger issues from seeing the way elderly relative monopolised all the time and spoke to their parent/carer like shit, not doing well at school so won't get a good job, life of poverty. The cycle continues.
You can't force people to become carers, it's kicking the can down the road. There's lots of reasons why people can't do it the above is just an example and why the resulting mess would mean more lives being ruined and cost government more in the long run and the elderly people still ends up in a care home.