Also the ratio is a lot higher in nursing homes. Yes you might have a ratio of x nurses to y old people, but you also need to consider the people indirectly contributing. Like the trades people who built the building, or the people who pay for the care through taxes or otherwise, the people working to route electricity, the pharmacists making all those medications that the old people need, etc.

Also, we need people to do jobs other than working in nursing homes. We can't have all our workforce caring for the elderly.