I work as an EMT on film and televisions sets, carry a lot of first aid/trauma gear in my vehicle, up to and including oxygen. For personal EDC purposes, all I usually carry around is a small zippered pouch with some bandaids; large and small, couple of 4x4's, sting-eze wipes, couple of BZK cleaning wipes, safety pin, tweezers and a small tube with some antacids and a couple of 200mg Advils.

I have a bandanna in my pocket that can be pressed into service as a pressure bandage if needed and I carry a CPR mask in a tiny pouch on my keychain.

The majority of stuff you're gonna use a first aid kit for in an urban environment is simple cuts and scrapes, splinters, and an errant bee sting.

If I had to try and carry my actual trauma gear around, I'd never go anywhere.