I can't imagine my parents wanting me to be locked out, and I can't imagine wanting my children to be locked out. Things like personal correspondence usually stop being private once someone is deceased, and indeed, are one of the few ways to get you know your ancestors.
I'm not American by birth, but I've lived in America long enough to understand both values. I don't think either way is better, but this strong emphasis on privacy (with family) is a very Western phenomenon. In most places, families have far fewer internal secrets.
What's especially odd is how much more Google and other corporations are allowed to know about Americans than families. For me, it's backwards.
Other things were also required. E.g. my father had a small business. It was big enough that it had real income and we wanted to keep it going, but not big enough that there was tons of redundancy for this type of event. Without having his passwords the business would have ground to a halt in 2 weeks (payroll). Add to that all sorts of business accounts (domains, mail, accounting, etc, etc) and having this emergency access turned out to be the key to keeping things going.
Even his personal email - he would have wanted us to have access, but how does he give access without just giving us his PW? Turned out that emergency access was the perfect solution.