On your mark, get set...

Well there is the classic "Drums set the tempo" style of time keeping, the conductor is more a necessity in grandiose melodious works where tempo isn't easily kept from the percussion alone.

Rock Bands, some Marching Bands, and arguably a bunch of Jazz Bands considering how much those conductors tend to devolve into just dancing around on stage like a possessed Muppet, are able to keep time without the visual cue the conductor provides in a less rhythm intensive composition.

Not to mention that developing an accurate internal metronome for others to build a song off your cue is a skill unto itself, as well as being able to read every part of the song at once to be able to properly rehearse the combined ensemble and tell if someone needs an adjustment.

The conductor as part of the rehearsal is always overlooked here. Music, especially ensemble music with 80+ muscians, can easily be interpreted in many ways. Even when the sheet music has guidance, there are always degrees to decide on. How fast to go here, what volume to play here, on and on, and generally every instrument has different requirements to make a piece fit together. Someone guiding that process, having an understanding or at least a point of view, is a big part of the job. The stick wagging is just the end point after all the other work is done, but it in itself is also useful for execution and consistency.
- So is conductor similar to film director or project manager, in that it seems pretty unnecessary for a small thing (which is what most critics imagine) but once it becomes complex and there's a lot of people trying to do different things at once then you need someone to keep everyone on the same page?
In concert, jazz, and marching band, I was always grateful for the conductor as a visual cue for timing. All of that "dancing" often tells you where you are in the music or how you should be playing. I briefly performed in a rock band and tried using a metronome in my monitor to keep on beat. It was so much more difficult than I ever realized and I had to have a recording of our music played into my in-ear monitor so I wouldn't get lost. What I would have given for a dancing possessed muppet rock conductor.
Conductors (drum majors) are absolutely vital in marching bands. Marching bands (both traditional military style and modern style) use formations so large that the speed of sound is a significant factor - trying to keep tempo based on listening to e.g. drums simply won't work, because different positions will hear the beats at different times (and that's not even considering issues like echoes, or the auditory dead zones that closed structures have). Having visual cues for keeping time is a necessity.

For even a medium-sized orchestra I think a conductor is required. In the end you need one person who decides the tempo and timings. Without a conductor a musician will have to play the part. Here's an example: https://youtu.be/oJ2ZLr87lLY

Clearly the main violinist takes over the role of conductor, but even then timings are off even in this short piece. And that's a trained orchestra with a well-known piece. A full symphony with a larger orchestra and maybe even a choir (like Beethoven's 9th) would sound terrible without a good conductor.

You 100% need a conductor.

Light travels a lot faster than sound.

So even if everyone focused on a single musician they'd all slip out of time.

And then pixelatedboat hears a conductorless orchestra for the first time...

grimaces and puts their hands on their hips

"...Not my fucking tempo."

There's a Dutch TV show based on this. A couple of celebs get out in front of an orchestra, which then plays exactly what they are conducting.

They do get training, but the first episode they know absolutely nothing.

It's quite insightful and teaches the importance of the conductors role and the amount of control he has.

I can't link right now but if you search for maestro tv show you'll find some snippets, I'm sure.

They're not wrong. If the piece has a load of tempo changes and pauses then the conductor is pretty vital but most music doesn't require one.

Even with a consistent, steady tempo, someone needs to set it and keep everyone the same. For rock and jazz bands, it's usually the drummer, but an orchestra isn't going to have a steady drum rhythm that everyone can hear.
It's not about the complexity of the music, but the logistics of getting lots of people playing in sync. A large orchestra is large enough that there will be fractions of a second difference between the more distant players. In some cases, the players literally cannot synchronize themselves via audio cues alone.

Also, good luck getting dozens of people to come in from silence at the exact same moment without a conductor. They're pretty critical when they're needed, which is very often for orchestras.