Bicycle clips were popular accessories on ten speed bicycles used before the advent of mountain bikes. I remember having a difficult time getting my shoe to remain inside the clip. The only good way to do it was to have someone else clamp the clip around the rider's shoe after mounting the bike. This also meant that the bicyclist was attached to the bike no matter what happened.
I do remember getting more power from the pedals whenever I had to climb steep hills, and the extra upstroke did make it easier to generate more speed on flat terrain.