But that means she’s not getting security updates and since she’s grandma she really needs them. On the other hand, if you’re automatically upgrading her Arch install then there will be breakage she is hopeless to fix.

True, but that would be the end result in any case where an update do something wrong or require some sort of manual intervention, it is not strictly tied to Arch. But you have a point here.

So what advantage does Arch offer grandma over a traditional release LTS distribution which will be nice and stable, not breaking or changing unexpectedly on her but still remaining current with security patches?

Only to have some newer software, but you can also update Arch every once in a while, the fact that it is a rolling release does not mean you need to update every day. The everything will depend on which distro normally uses the person who install the grandma machine