If you’re a chorister standing in a gallery quite a distance from the stage, as I often have to do, then you absolutely have to have a clear beat from the conductor to keep in time. Waiting for the sound of the orchestra to reach you means that you’ll always be behind the beat. Perhaps only marginally behind at first, but the delays accumulate quite quickly.
You’re thinking of Jean-Baptiste Lully (d. 1687). I don’t think Lully’s fate really had much influence on the replacement of the conductor’s staff by the modern baton, though, which doesn’t seem to have really got going until the early nineteenth century.
Anyway, if you really want to get an idea of what difference a conductor makes, listen to recordings of the same piece by two different orchestras. (Sometimes classical music shows play extracts from different recordings of the same piece side by side when they’re analyzing different conductors’ interpretations, too.)
It does make a difference when you get out of orchestras and into marching bands. That field is pretty big and lag is a real problem, especially if you’ve got a speedy song and a spread-out formation.
The story is of the death of the composer Lully, who did indeed die from a gangrenous foot injured while conducting. However, both evidence and common sense shows that most music in most contexts used more subtle gestures, with the hand or with a held object used to indicate a beat.
Oh, pshaw. Any system that calls a whole note a “breve” (short) and a half note a “minim” (least) is missing a beat or two in the logic routines.
So, if looking back and forth between the notestand and the conductor is vital and difficult, has anyone tried something like an optical repeater of some sort (a LED or something) on the notestands, controlled by the conductor? Or a HUD for musicians, superimposing an image of the conductor on the music sheet? (I know, that’s thinking like an engineer not a musician…)
Well, most people think of a conductor as just a sort of ticket clerk who walks up the train collecting tickets…
What?
Maybe not half a beat, but enough to make a difference.
End to end, a decent sized symphony orchestra setup is about 65 feet across. This is a delay of a little over 1/20 of a second for a sound originating at one extreme to reach the other.
If that were a half a beat, then a beat would be a little over 1/10 of a second, and the actual metronome tempo would have to be 520 bpm. Describing this as a tad Vivace is an understatement.
But we don’t need music that fast to create a problem. Because if someone on one side of the orchestra is attempting to time his sound to someone across the way, the person across the way is timing themselves to our first player, so the delay is doubled for sound transit alone, never mind the time it takes to hear the sound and get one’s own note out.
It’s also the conductor’s responsibility to, when the solo soprano is consistently flat on the high notes, stab her in the eye with his baton.
</not really but wishing>
I’m going back to my earlier analogy of the backswing. A light doesn’t give you that. The absolute timing is only the first step to being a good conductor. Beyond that you’ve got to be able to communicate with every member of the orchestra (aurally, visually, etc), and be aware of everything that is happening. While also being aware of what should be happening in the music.
Edit:
As I say to pupils: “I have a thorough explanation for all of that. I could tell you al about it, or lend you a couple of books for you to read, or we could just accept that 6/8 means two beats in a bar”.
I feel bad about it, but haven’t found a better way.
Going along with what GorillaMan said, lights on the stand would be bad as performers should be looking at the music as little as possible; when they know a piece well enough they ought to use it only so they don’t get really lost, or as a reminder of the upcoming phrase they’re about to play.
Some marching bands don’t perform with sheet music at all; but then some do use multiple conductors to keep the beat (e.g. when facing the opposite side, or specifically to help out the drummers). Sousa famously conducted 6/8 by merely swinging his arms
(and then some aren’t conducted by a Drum Major … hawksgirl, are you in the band-uh by any chance?)
darn! outed again! 
Stick?!
Baton, sir, baton
But the conductor isn’t just a human metronome. If that were the case, they could just use a click-track (everyone wears headphones that play a metronomic beat) and dispense with the conductor altogether. The conductor is also showing the mood, dynamics, and style of the piece.
Your idea is done in recordings, except an audio beat works better than a visual one, because it leaves your eyes free to focus on the music.
Dang, how much would it cost to have that for every stand in the orchestra? And it’s not the distance between the music and conductor that’s the difficulty, it’s being able to multitask. Having both images in the same spot still wouldn’t enable anyone to concentrate on both simultaneously without years of training. Besides, I think it would be more of a distraction than anything else.
They do have electronic music displays now, though. Instead of sheets of music, you can have a screen that displays an image of the music. You can “turn” the pages with a foot pedal.
Pshaw yourself. A breve is a *double * whole note. Anyway, whole by what definition? The second movement of Beethoven’s Eighth uses a tempo that would make a semibreve a ridiculously long “whole note”.
Y’all should know that historically - or in antiquity anyway - a breve was a short note; back when long notes were used for reciting lengthy passages of words. But the “long” isn’t often seen these days. 
In my view dropping historically interesting words simply for the sake of adopting a so-called rational system of taxonomy is doubleplusungood.
So much more convenient than a hand pedal.
Yeah, I realized on my way to rehearsal last night (for my thoroughly American choir with its thoroughly English director. He’s come to terms with eighths and quarters) that I had screwed that up. It doesn’t precisely weaken my point. And the definition of “whole” I assume comes from a “whole” bar of cut or common time. I’m not sure what Beethoven’s Eighth has to do with anything.
And in my view, holding on to illogical antiquated systems that lack logic or consistency* is not exactly doubleplusgood. We could also do away with barlines and the five line staff if you want to genuflect to “history”. I don’t really see the point, though.
*The quarter note, eighth note system fits much better with the standard system of metric notation. Six-eight means six eighth notes, not six quavers. Although really, Orff’s system makes the most sense.
For the record, I have no difficulty with crotchets and semi-quavers and whatever you want if that’s the system you prefer. It’s easy enough to translate, and any musician worth his salt knows what they all mean. But I prefer to live in a world where two eighths equal a quarter, rather than two quavers equalling a crotchet. It makes about as much sense as feet and miles.
Surely a conductor is merely something that has a large quantity of readily mobile electrons?
What? What?
I think most rock musicians, certainly my bass teacher, feel that the bass player fills this role. I can imagine good rock music with great bass and a click track but if it has good drumming and no bass how could it be rock?
Its easy to check out. Wire your speakers out of phase and wind all the bass down and most modern music becomes entirely listless.
Simply that there’s no way a semibreve would fit as a “whole” note the way he wrote it (the second movement). It’s years since I played it, but I remember our astonishment on seeing hemidemisemiquavers (sixty-fourth notes, which you and I both know but I explain for the audience) in the score. IIRC the time-signature is 4/8 and most of the notes are semiquavers. Similarly the “whole” note designation is arbitrary - it’s not a whole anything in any kind of triple and/or compound time.
Mind you, I’ve seen a musical dictionary that agrees with you ad nauseam.
Sure, and I can cope with talking about half-notes and quarter-notes and so on. And I personally cope with the breve-to-hemi nomenclature about as well as I deal with inches to feet to yards to chains to furlongs to miles… (in other words, effortlessly).
Still, I agree that in the ideal world we’d talk about small-fiddles and middle-fiddles and big-fiddles - and all our dynamic and tempo markings would be in English as well, I mean, who needs to dick around with “Allegretto ma non troppo”? 
On the rehearsal/“style” issue, I’ve heard a number of pieces performed by different orchestras, following what different conductors wanted to “get out of them” in rendering it, and it can be remarkable how his emphasis on specific passages turns the piece into something audibly different. Smetana’s “The Moldau” is the one that most stands out in my memory, but to take a piece that everyone over the age of 3 has heard, the 1812 Overture as performed by the Boston Pops, the Syracuse Symphony, and the North Carolina Symphony is effectively three different pieces of music, even though they all are playing the same sheet music with the same or similar orchestration. It’s simply remarkable how a difference in focus and emphasis will reshape what a piece “says” in that way.