I think the show failed solely with the absence of Dorothy. She wasn't the "leader" (as the OP puts it), but she was the 'anchor'. She was the snesible one, the wise one, the one who saw things clearly among the four. Without her, there was no anchor for the ship.
I don't think it would have been so devasting (and the premise probably could have worked) had Dorothy stayed, but one of the other girls left. They could always have a regular/semi-regular who was naive and ditzy (Rose), the southern sexpot (Blanche), or the cranky elderly 'mother-figure' (Sophia).
Not as easy to have someone step in as the constant anchor to keep them going astray - and that's exactly what happened to the show. It went astray, rather quickly.