Oddly enough, Grease was the most demure I've seen her.
I don't want to beat a dead horse, but...another 2 Gentlemen story.
I was exiting the theater through gate 1 (where the actors entrance is) during intermission. Grigsby was walking through, in full costume (backless shirt, etc.), and two older gentlemen, drinks in hand stopped her and told her how much they were enjoying...looking at her.
Part-time pit musician here. Just want to second what markymatt and ilovemydictionary said above. Of course, there are some parts of some numbers that can (and do) sort of go on autopilot, but SOMEONE has to cue the fermatas, the end of vamps, tempo changes, etc. You'd be surprised how much is actually cued to the dialog and the stage action, and how much all of that can differ from night to night, and you can't have 16 different people deciding. In smaller ensembles, the keyboardist, for example, may give the cues, and not actually conduct throughout, but there are still lots of hand gestures, head nods, etc.
Point blank- where there is a group of sometimes up to and over 20 musicians, there needs to be a conductor. Aside from the obvious (keeping time, giving cues) the conductor is in charge of everything musical for the performance. What if a singer comes in at the wrong time? What if they miss a cue? If there was no conductor, the orchestra would be completely out of sync with the singers. Half the time, the only person who can see the stage is the conductor, so they're the middle man for the orchestra and singers.
Coming from a budding pit musician- I'd like to think of it this way- there's always a conductor at a professional orchestra concert. The CSO doesn't just get up and play. The same is true for a pit orchestra. The conductor is responsible for rehearsing the musicians and interpreting the score, and in performance the conductor is vital, not only for tempo. Typically, instrumental music is the conductor's medium, and even if there are actors who are in control of their own performances singing onstage, the orchestra has to act as a unit, under the direction of the conductor, in order to make the singers sound good.
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.