Not unless you want to or someone does it for your own benefit. Especially if you play an instrument where getting a baseline level of competence in reading and playing written music is all you need to be able to do to be part of the ensemble, and especially when it's a relatively casual ensemble like most high school bands.

Not just theory though. I've met people who continue to perform in orchestras decades after high school and college, who play with really good groups, and who have literally no interest whatsoever in the music they play, let alone its theory. It's always bizarre to me to talk excitedly to someone about the piece their orchestra is playing to only be met with confused indifference about it and the composer. For some people it's just an activity to keep busy and nothing more. This is not necessarily a bad thing, it's nice that there are many ways to engage with music and be able to choose how involved you want to be.

In the US, theory is typically part of post-secondary musical education. Some high schools might have it, but in a lot of high schools filling out the marching and symphonic bands with warm bodies will drive a lot of a music program.

Typically, piano is part of post-secondary music program requirements and keyboards make it practical to apply music theory to make sounds...arpeggiation will get your ear so far. Polyphony gives a much clearer picture of what music theory is describing.

If you're interested in learning music theory, a polyphonic keyboard that makes sounds without a computer (maybe one with speakers, but at least with a headphone jack) is my recommendation. Maybe it's better if it is small and portable. A MIDI controller with a phone or tablet might be ok, but phones and tablets have email and the internet and those can interrupt what you set out to do.

Anyway, theory usually comes later in the US system. There are exceptions of course.

Yes, and yes. The reason you weren't taught much theory is because on a horn you're only playing one note. But I think that's really a shame, because you were deprived of the understand of what you were playing and why, in the context of the notes and chords that the rest of the band was playing. And even when playing a horn solo piece, there is always an understandable, chord-based structure to the piece.

Edit: Also it really doesn't take much effort or theory to understand most of what would be interesting. Like many subjects, the 80% of what's helpful can be written on just a few pages and learned in a few hours - but whole college curriculums can be made of the details and nuances. Go read up on 7th chords, cadences, and simple chord progressions if interested.

This is an oversimplification imho. Many of the greatest jazz musicians like Miles Davis and John Coltrane played instruments that could only play one note at a time, and they still manage to convey harmonic concepts.

I don’t have an answer for why most music teachers don’t teach theory (and improv) other than it’s more challenging and they might not know it themselves, and it’s easier to teach rote memorization.

There are plenty of people who learn piano (which obviously doesn’t suffer from the single-note “limitation”) and also learn almost no theory.

Horn players can always outline chords, perhaps with outright arpeggios or by choosing chord tones on downbeats. That said, even if your teacher had armed you with theory its still just comes down to an assload of work. But maybe that might have helped you connect with a feeling of reward.