Backward bycicle, SmarterEveryday.

I've done this with guitar on my early 20s. I'm righty and one day just decided to locked-in like Destin did to see what would happen. And like him it got to the point where something's flipped and I could strum open/barre chord comfortably but didn't get too far with melody though, picking hand is by miles much more awkward, orienting and holding the pick the right way is much more precise control than I thought. I could do decent enough legato to fool non-player.

Then I stopped for a week and it's just gone, I didn't become ambidextrous.

Picking requires much more control than fretting once you've learned the basic shapes or movement.

Think of the timing in it. The fret can be pressed at any time between two notes, but the picking needs to be exactly on time. Fretting basically becomes muscle memory while the picking is the real decision making.

Also think of the expression. Once you've fretted a note, there's little to do with that finger. Bending and hammer-ons maybe, but it's nothing in comparison to what the picking hand does. The picking can change the volume, overdrive, pinch notes, muting and overtones depending on position. Also of course timing as already mentioned.

Traditionally, it was probably chosen because of finger picking though. A lot of classical music is based on very basic chord shapes while the picking hand does all the coordination of playing both bass and melody simultaneously. That requires a lot more rhythmic independence on the picking hand than the fretting hand.