What's wrong with having the black monitor that came with it?
Well, nothing, but not many CDTV's came with a monitor! If you got one with yours, great, but that was a package deal, as most (probably better than 90%) CDTV's were not sold with a monitor and the owners just hooked them up to their TV sets.
I wish my CDTV had not quit working. Other than the original A1000 case, I like the CDTV, but it should have had a wireless keyboard with trackball as standard equipment instead of just the CDTV remote controller. A wireless joystick would have been good too, as the standard wireless controller is not as good for a lot of Amiga games IMHO.