Getting rid of dispatchers is a big mistake if you ask me, but of course being one I maybe a bit biased
But I have never seen it as being a good thing.
For example I was a dispatcher for KLM and we were working closely with Air France who did not use dispatcher on its AMS flights but iso the role was partly done by ramp staff, partly by Passage staff...
Their punctuality was crap where ours was excellent and AF was the first to agree that it was because there was one person in charge of the flight and not three or four different ones