Apart from the fact that a convertible is designed to be convertible, ie used in both manners, you can feel the air con with the roof down anyway. Put it onto your feet and it flows over you.
I wouldnt want a convertible which wasnt usable with the roof up, for example on the way into the office suited and booted with neat hair, driving down the M4 into london, i dont want to be sweating my shirt out.
Surely you get that?