Hi Martin!
Depending on the event i'm being assigned to, I might carry a team-supplied Heartstart AED and o2 tank in this bag. I might not have given enough context when I described my story at the beginning of my post. I am part of a volunteer group that offers first-aid services to the community. This group is structured, members wear uniforms (etc.) and our training goes beyond basic first-aid (AED, o2, airways, etc.).
I understand that for a «normal» person that gives first-aid care twice a year, a trauma bag with it's corresponding looks might be pushing it a little. However, at the end of the day, in my context, I think it's alright. Like NightHiker said, if the bag is a trauma bag, it should be identified as such so it's not mistaken for something it isn't.
Thanks and have a great day!