Hope you don't mind me jumping in with my 2c worth alophysio!

If we are looking at function for an athlete, then it is important to realise that knee extension never occurs in isolation. It most commonly occurs with hip extension and ankle plantarflexion during concentric actions in order to create movement (seen in athletes during jumping, running, accelerating etc). You will also see the quads working eccentrically to decelerate movement at the knee (along with the glutes and calves to decelerate the hip and ankle), which will be seen on the athletic field in stopping, changing direction, as well as the preparatory phase of vertical leap and in landing.

Most of the strength of these muscles will be used when the foot is on the ground, very much unlike a knee extension machine. When preparing athletes, I prefer to use Schultz's classification of functional human movement, which for the lower limb would transfer to:
Squat
Deadlift
Lunge

There are also tons of variations that you could use to keep an athlete progressing. Here are a couple:
Squat: Back sq, Front sq, Box sq, Zercher sq, Goblet sq.
Deadlift: Regular DL, Snatch grip DL, Romanian DL, Stiff legged DL, 1 legged DL.
Lunge: Split squat, forward lunge, rear lunge, lateral lunge, rotational lunge, step up, lateral step up, Bulgarian Split Squat (my favourite!), single leg squat.

One should never play down the 1-legged movements - how many athletic movements actually use both legs in the same way simultaneously? Jumping and rowing are the only ones that come to mind.

Obviously, this discussion has shifted from the original question, but if a high level athlete develops patellofemoral pain, these are the movements I would be looking a t getting back to being able to perform pain free.