Why cant the human body bend fully down without bending its knees?

You have to keep your center of gravity over your feet.
If you can bend your ankles backwards enuf to do that, you do not have to bend your knees...
If you are up against a wall then you cannot do that. That is, your backside cannot get far enuf away to balance your upper body to keep the center of gravity over your feet...

 


I believe the question is fundamentally flawed:

Many people can bend down fully, without bending the knees. Personally I can bend down far enough to put the palms of both hands flat on the floor simultaneously, while keeping both knees locked with legs fully extended.

With reference to the image you have posted, the ankle joints allow the straight legs to rotate anticlockwise, in a motion approximately parallel to the mid-line vertical plane passing through the torso, during the bending down motion, thus allowing the legs, buttocks and lower torso to maintain equilibrium against the weight of the upper torso, arms and head.

The manoeuvre maintains the red star in the image in a vertical line above the region of support formed by the feet.

https://www.youtube.com/watch?v=n4YCG4k0Q6o