Good points, and I'll just add it's not just family who can infect grandma, but the staff at the facility, who also have kids and family, and who are out in the world, half of the sick don't show symptoms, and those that do often take days after infection to develop symptoms, so a quarantine of the elderly in nursing homes requires the workers to quarantine, and their kids, and their spouses, along with nurses at doctors offices, and delivery people, and maintenance workers who visit the facility, etc.
That's why where there is wide spread of the virus in the community, nursing homes get hit hard. One follows the other. Sweden let the virus spread, and they lost a lot of old people in nursing homes. Those aren't independent events. Aggressive testing of staff and others can help, but that was not possible early on. Etc.
These arguments - just protect the old - are IMO nearly always dishonest, or at best ignorant. It's easy to say - reverse quarantine the old - but get into the details for 5 minutes and lots of MASSIVE barriers are obvious. My mother in law's place had one infection. It was from a resident going to the ER for something, getting that taken care of then admitted back home. They tested her at admittance and it was positive. Well, you can say - don't let her back in! - but then what's the option? Her HOME is that place, and there's no facility set up to take her and isolate her for two weeks. So CDC and the state allows her to return, but with a bunch of restrictions, more PPE required for everyone who deals with her, and more. And it worked.