Depends on what you mean by 'a purpose'. I think when they are done well - by someone like Michael Parkinson - they provide simple entertainment from an erudite and witty guest. When they are done badly, by someone like Clive Anderson, they provide a guest who will attempt to answer a question for as long as it takes for Clive to remain powerless to resist his ego's desire to score a cheap point, or try to look clever and sharp. This type of 'chat' can backfire - witness the delightful spectacle of The Bee Gees voting on Clive's 'wit' with their feet - now that was what I call entertainment!
As most current chat shows seems to be an excuse to plug the guest's latest film, book, CD etc. the answer would depend on how many people go to see the film, buy the book or CD, or am I just an old cynic?
The evening ones provide a cheap way to fill airtime with no creativity required. The daytime ones are a substitute for religion as the opiate of the masses. I can think of few sights that would give me greater pleasure than that of Ricki Lake and Kilroy being sealed into an airtight box so that they could patronise each other until the oxygen ran out.