The conductor is absolutley necessary for all of the reasons so far mentioned, observing fermatas, cueing after vamps, etc. In the past, if a show had a true star, the star's tempo had to be adhered to by the conductor, not the other way around. I'm fairly sure that Patti LuPone set the tempos for her numbers in the recent GYPSY run.
The conductor has traditionally done the vocal arrangements for any chorus numbers, and such a chorus has to be conducted, too.
I've posted this annecdote before, but it is applicable here:
When Rosalind Russell was appearing in WONDERFUL TOWN in 1953, she would be standing in the wings waiting to go on, thinking, "How am I going to do this show again tonight?". Then she would be on stage, looking down at pit conductor Lehman Engel's smile of encouragement and she would feel reassured that all would be well. So, the conductor is an important provider of support and encouragement for the performer.
"Madam Rose...and her daughter...Gypsy!"