is it a good idea to carry personal insurance even if the facility you work at covers you?
Yes! The facility, no matter how respectful and honest, is always going to look out for themselves first. Your own policy will help to cover you and look out for only you. Plus, like others mentioned, the coverage is not that expensive.
Better to have extra coverage and not need it, than to have something happen and find out that the coverage you thought the facility had for you, isn’t there!