I don't know if there's a common expectation?
I dread needing care for my family or myself. Most people I know feel the same. Too many times I've seen news reports on care home abuse, only discovered after a concerned relative installs cameras. I've told my family I'd rather have assisted dying but that's my choice (and something I want at that stage of my life even if every care home was excellent). However my choice should never be expected for everyone. Compassionate care that doesn't cost a fortune should be possible. It used to.
When I was a kid an elderly relative was in what was then called 'an old people's home'. She didn't need nursing care, just a bit of extra support, but It was a mixed needs home. It was a lovely place. Safe, homely environment with good community feel, sense of companionship with other residents, variety of activities for residents, welcoming communal spaces, and kind empathetic staff.
Didn't cost a fortune either, and although wages weren't high there were no staffing issues. Because there was more affordable housing in those days, but also management treated staff well. Staff didn't have unbearable to manage workloads, and residents who needed nursing care had properly trained staff to help them.
Something's gone wrong. Care home costs are skyhigh, and (good) at-home carers are often even more expensive. The problem is the lack of affordable housing, but also I think it's the privatisation of care homes and care services.
With family caring for elderly relatives. In the past there were more SAHP so this was more possible. Now the cost of living especially housing means few can afford to give up work to care for family. This is yet another issue linked to the lack of affordable housing. Related to this is many people have had to move away from family for housing or work.
More social housing and better job opportunities in all parts of the country would help, but there's also the issue that many people have nursing needs beyond capability of their family. They need properly trained professionals. However definitely if there was better financial support for carers and affordable housing, I assume more people could care for family at home.