Depends on what you mean by "care for". Calling your parents a few times a week to make sure they're doing OK and dropping by on the weekend doesn't take too much time and effort. But as people get older they need more and more care. Caring for one person with dementia or other similar problems that comes with aging is for all intents and purposes a full time job.
And eventually if you can't afford to become unemployed to do it or pay full time caregivers, you need to move them to some kind of care home where there is minor scaling effect. Being housed together, the residents can share caregivers since most do not need continuous help.
A common arrangement is a board and care home with about 4 residents and 2 caregivers who work mostly non-overlapping shifts, and one sleeps onsite to (hopefully) be able to handle overnight care needs.
A larger place can scale a bit better. E.g. 10-20 residents can have 5-10 staff on various shifts. But some staff could be cooks or handle cleaning while others focus more on the residents' needs. And at this level of staffing, they can manage to have an overnight shift with someone who remains awake to keep an eye on things, as well as probably having other(s) sleep onsite to be on call to help with bigger events.
I agree with you, but I read the article as saying you can't care deeply about more than one person at literally the same instant. Your attention is directed to one or the other.
But I think even that's not literally true e.g. the social worker could make dinner for all four kids at once. And probably converse with all four of them while doing it!
But, I think I agree with the broader point that care doesn't scale, even if it does scale slightly greater than 1.
People have children, in this world we can only care about our spouse or one child?
Hardly.