I'm stuck. Can't figure out how I can extrude a closed curve onto a NURBS curve without it looking tapered.
I notice that when it's set to "2D" there is no tapering, but I want to do it on 3d.
It's a known limitation of the current system, there is currently no elegant workaround for this as far as I know.
Choose the lesser evil for your particular use case.
In the Object Data tab in the Properties panel (pictured in your screen shot), under Shape > Resolution: > Preview U:, change the number from 1 to 64 (the max). Leaving the Render U: at zero will cause it to use the Preview U: (just fine).
Also, make sure that you have added enough loop cuts to your cylinder so that it deforms properly.