Same for credit cards that offer travel insurance as long as the flights/rental cars etc. are booked through them. They'd most likely need to see the charge from the airline in order for the coverage to be effective.
The trip insurance card benefit— I don’t think we can satisfy right now. We’re exploring ways to use the user’s own CC with the end vendor (eg airline) rather than us charging the user separately. “credit card tokenization” should work here (Spreedly, TokenX) but it’s non trivial due to how many vendors are in the space
Email me if either of these are stopping you from wanting to use the service, and we’ll figure out a workaround or let you know when it’s solved!