@PotomacBob
a 13-year-old eighth-grader (middle school) trumpet player performing solo for the first time with an award-winning high school orchestra
I know a little about this, but I'm not an expert. My understanding is as follows:
The purpose of the conductor is to get all the different instruments making their entrances and exits happen at the same time and at the same tempo - and (to a lesser extent) to maintain that tempo throughout the piece of music. They also use signals to get everyone following the dynamics of the music in the same way (though a lot of that is worked out in the rehearsals). In other words, their gestures to have everyone build the volume as they approach a climax will ensure all the different instruments build volume at the same rate.
In this specific instance, no matter how good the trumpet player is, and how well they know the music, they have no way of knowing the tempos - and change of tempos - that the orchestra uses for that specific piece of music. That's what rehearsals are for.
Many students (even in an award winning orchestra) have trouble maintaining an even tempo as they play - particularly if their individual part is tricky, so the conductor provides them with that steadying tempo that they can stick to.
Keep in mind that a high school orchestra (even an award winning one) will be made up of students who have only been learning their instrument for a few years. Professional orchestras often include musicians who have been practicing their skills for decades. When it comes to making music, time spent practicing really does make a difference.
And most such professional orchestras still use a conductor.
If a soloist is playing completely on their own (without the rest of the orchestra providing backing music) and their individual timing is good, its not uncommon for the conductor to stop conducting until its time for the orchestra to rejoin.
Conducting an orchestra takes skill and practice. As I understand it, part of the trick is you have to mark the beat a split second before the sound (because it takes time for the musician to blow and the sound to come out). I've known experienced musicians to go and take lessons and practice and practice before even stepping in front of a rehearsal, let alone a performance. I've also seen teenaged musicians, with only a little bit of practice, successfully conduct their peers through pieces of music, and literally learn as they go.
A person who just "likes the music" would tend to "conduct" by following the music rather than leading it (ie they beat as the sound hits them which is a split second after the musician blew into the instrument) so they are actually distracting the musicians rather than being helpful.