Either way, it's not really negotiable with a judge, so your approach is a little misaligned to how it works here. We generally have to take care of these things here in court, which is obviously quite inaccessible to you.
So ultimately you're right - things work differently here than they do at home for you when it comes to statutory violations. Police in the US can be very strict about things you view to be trivial, especially in low population areas, as you noted.
Honestly, if I were you and planning to go back, and especially to Utah, as noted above I'd ask for the warrant to be vacated and pay the fine.
Viel glück!