Travel Insurance and Amex Platinum
 

That is not enough information to give you good advice.

First, sit down and read the policy terms (the complete document) detailing the coverage and determine if there any "holes" and what those might be.
Second, we don't know where you are located or what you consider to be longer or bigger?
Third, are you worried about a night in a motel or are you headed to Asia and might need medevac (which could cost $200K or more0?

Once you figure out what your included coverage is and what you need, then people here can provide great advice based on real life situations.

Welcome to Flyertalk. If your card is issued in the USA there is no comprehensive travel insurance for risks such as delayed flights or cancelled trips. The answer would be very different if your card is issued in another country.