Well, using science we could construct a study where a large scale community has many services pro died by humans vs another large community where many services are provided by automatons. We could look at the strengths and weaknesses of both and maximize human happiness and well-being.
The result could be as simple as machines just fill in gaps for when were tired, moody or on vacation. We could optimize for min usage of automatons, and target low performers for educational opportunities and psychological support.
I much rather have window cleaning and fixing road pavement automated than looking after my kids and the elderly. I doubt that the machine or robot will be able to convey the empathy required for people interaction.
The robot is not going to molest my kids and the elderly. The Robot will not cough tuberculosis spores onto them, will not touch their food after picking a nose or wiping an ass (both of which the robot lacks), and will not brush them with herpes sores. When the robot dies, an exact replacement can be had. The robot will never decide to kill out of frustration, religious fervor, or revenge. The robot will not steal.
But those are jobs where personal contact matters, and that's not easily automated. By all means automate the hard/annoying/disgusting parts that can be automated, but still add people for the personal touch.
Today, due to the low amount of money we're willing to spend on care, and the high demands and pressure on the people providing that care, people who care for elderly and sick people often don't have the time for personal contact, often to their own frustration. So let's automate everything else so people have more time for real contact.
I think you're dramatically underestimating the cost of providing personal care. It's incredibly expensive because it's so labour intensive, and as you point out it's the personal part of that which matters, which makes the costs so hard to reduce.
The result could be as simple as machines just fill in gaps for when were tired, moody or on vacation. We could optimize for min usage of automatons, and target low performers for educational opportunities and psychological support.