the noise to weight ratio
is not acceptable to me. the little bit of weight is well worth the drop in outside noise, etc. not will you lose the sound dampening, but it will actually be amplified by reflections.
just my opinion though. i have seen cars that run without and it can be a cool look. i was going to clean up the channels and run a c/f headliner, but bailed for several reasons. one was i decided to go with a ragtop. the other is that it would do nothing but reflect sound, much like running with no headliner.