The premise is wrong, you can care for more than one other person at a time.
People have children, in this world we can only care about our spouse or one child?
Hardly.
People have children, in this world we can only care about our spouse or one child?
Hardly.
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.
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.