you should actively pull up your leg so the down leg is not working extra to lift it, and the pull up muscles are different muscles so your idle down muscles are still getting a rest.

The pulling up of your leg results in easier pedaling overall, and it is relatively as if you are pulling up on the pedal. Should you actually then pull up? You should go for the most natural sustainable pedal motion for you. When I pedal I "visualize" my feet going in circles, not up and down, it helps me on the "over the top" and "across the bottom" parts of the circle. keeps me sinusoidal!

If you never pull up at all and you are pedaling and feeling tired, try pulling enough to remove the dead weight leg from the equation and you'll feel rejuvenated.

Honestly, go try biking by only pulling up. You don't pull up.

Bike more and you will, it's not particularly noticeable while normally biking. But I really notice it on sprints, but it's also noticeable even with smaller increases in effort over cruising.

It's also quite noticeable when you switch to clipless and go for a hard ride, suddenly new muscles will be sore.

Honestly, I pull up. I'm not pulling the pedal up, I'm lifting the leg and pulling my foot up, getting it into postion to push again, same as I would do for running.

you should try it, you can feel the relief in the pushing leg.

I'll go try it. Why couldn't you do that in flats?

You do it with flats too. Clipped in feet just makes it so you don't need to worry about where the foot ends up after that. But it's not a huge difference.

Just do one-legged drills for a bit. You definitely pull up when doing this. Transfer the same muscle activation to two legged cycling, and you're pulling up then too.