A reminder

My band teacher would lose his mind if anyone did the tap with his conductor's baton

The conductor has several jobs both during rehearsal and performance.

During rehearsal, their main job is to cross reference what it's being played against the score and identify mistakes or areas to improve upon. These points are then provided back to the group and problematic areas are focused on. This may also identify times where some parts have a long rest and would benefit from being brought in at the right time.

During a performance, any mistakes will not be noted down, as they will be providing timing for the group, to aid everyone in staying in time and providing the initial tempo, and any variations in tempo (eg rall). They will also bring in parts as identified in rehearsal to avoid any counting errors.

Notably, they do not tell people what to play, as they either know it by heart or have it written down in front of them. They may settle any engraving queries during rehearsal if something sounds wrong, but that is the extent of it.

If you have any more questions about playing in a group or conducting, feel free to ask me, and I'll try to answer as best I can.

In addition to what others have noted, even if you know the music by heart, you are probably wearing ear protection, especially if you are in percussion.

So visual cues from someone actually hearing things will make it easier to do your part when needed.

the conductor keeps time, communicates dynamics and rhythms that are more subtle than what is written on the sheet music, listens to everybody to keep the ensemble balanced. there's a ton of nonverbal communication. this is more necessary in classical music where tempo moves around and there isn't a ton of percussion to follow. in jazz, especially smaller groups, you can listen to the piano and drums to follow the tempo. but with 60 plus musicians, it's really difficult to stay together when the tempo changes throughout a long piece.

Likely the players do not know the song by heart, and are reading the music instead. You still have a conductor if everyone has the whole thing memorized, though, to keep everyone together. By the time you are performing, the conductor is mostly ornamental -- they do keep the beat, but if you're a professional musician and you don't already know where the beat is, you're hosed. Most of what the conductor does is rehearse the orchestra. The musicians will read and practice the music themselves, and then the conductor brings them all together and had them practice important or difficult passages, and explain how they want the different parts to fit together, or stylistic changes they want. For younger musicians, they may also rehearse difficult passages to help the musicians practice, but as you get older and more skilled, you're expected to do that on your own. When you go to watch your local symphony, the conductor is basically dancing and it's more about conveying emotion and pulling the tempo faster or slower.

He takes credits and bows

What’s the point of a movie director? Do the actors not know the script by heart?