Why do we blink instead of winking each eye independently?
Looking at it completely in terms of evolutionary pressure:

1.1 The whole idea of binocular vision for humans, (and some other species) is depth perception. If you suggest continuous, alternate winking, the cognition of the individual would be seriously affected. 
The 'wink as needed' mechanism (assuming all other visual processes are as they have evolved today) would be like continuously alternating between a pair of binoculars and a telescope while still trying to move forward. 

1.2 If you are suggesting that there would still be an evolutionary pressure for winking, then its very likely that the evolutionary pressure for coordinated motion/ efficient cognition acting together with the evolutionary pressure for depth perception would be much higher as compared to it. (This would especially be true if eye-brain coordination evolved before the blinking mechanism, as is seen to be the case, which explains your point on 'how we are rather than how we got here'. Obviously fish have evolved some eye-brain coordination, but don't blink)

This link explains evolutionary pressure for depth perception/stereopsis to an extent
https://en.wikipedia.org/wiki/Depth_perception#Survival

2.1 As for the chameleon, the winking/ eye rolling mechanism might be very closely linked to the evolution of chameleon vision. It is seen as the link for studying evolution of binocular vision and stereopsis(depth perception) from monocular vision.

https://en.wikipedia.org/wiki/Chameleon_vision