I don't carry any first aid stuff (unless we are touring) but I did do a sport specific first aid course last year. It was part classroom and then out in the hills on moutainbikes simulating incidents of increasing difficulty/increasing isolation from services and phone signals. First aid being carried out on the floor of a scout hall is hard enough, but if you have someone on a steep hillside, lying in a less than helpful position, it does need extra thought.
It did suggest carrying minimal kit (triangle bandages, rescue blanket etc.), but was aimed mainly at using what you had on you - jerseys, pumps, forks, wheels bags, tubes etc, to stabilise the injured until either they could be moved safely or further help arrived.
I can highly recommend it, even just for the confidence it provided