Our troop had a few approaches.

On "small" trips (overnighters, day hikes, etc.), the scouts each had their own PSK. The creation of these was part of their training. Our older boys were formed into a high-adventure patrol so there skills and attitude filtered down to the younger boys. Most carried a store bought kit.

For bigger trips, the troop had a large first kit that was in a tackle box-like container. We had a large troop trailer, so carrying it wasn't a problem.