cooker

When you push down, you have both the force of your strongest and most efficient leg muscles, and the dead weight of your leg pushing down. On the upstroke, you may have some slightly less efficient muscles pulling up and one of their chores is to lift the dead weight of that leg.

Most riders probably pull up to some degree, but most of the time, as all those charts have shown, the muscles pulling up only serve to partially lift that leg. Any extra force needed to lift that leg, and all the force going into propelling the bike, comes from the downward pushing leg. Nevertheless, pulling up does contribute to propulsion, since more of the downward leg’s effort goes into propelling the bike and less into assisting in lifting the other leg. So lifting up is not wasted effort.

If you deliberately concentrate on extra pulling up, you can ride a little faster, but it is not as efficient as concentrating most of your efforts on pushing down, so you won't sustain it as long. You get more miles per breath if your ride in your preferred style, or concentrate on pushing down, and don't deliberately try to pull up harder. As I said, you probably are pulling up a bit anyway, but only enough to assist in lifting that leg, and much less than you are pushing down.