Wheel rigidity, is it noticeable and should I care about it?
For the average rider the answer to 'should I care?' is probably not.  If you are racing a lot of time trials then it's possible that it will make a difference.

Some of the primary benefits of a spoked-pneumatic wheel are traction and shock absorption. There is a trade off between increased rigidity (as well as higher air pressure) and both of those benefits.

So, a high rigidity wheel may increase energy transfer, and decrease rolling resistance. At the same time the harsher ride is going to increase fatigue, and the added vibration over anything but the smoothest surfaces will result in a decrease in traction.  Overall for the typical rider it's probably a wash.

It's largely the same story for the Aero benefits as well.  Unless you are primarily concerned about going fast in solo efforts the benefit would be minimal.