“it doesn’t need to go over the horizon to disappear in the distance”, but the problem is that it does go over the horizon rather than disappearing, as anyone who’s seen a sunset can attest

whichever way pisses off the most people

watch me pronounce it /χäɪf/ (“hyfe”)

on top of that, ‘e’ is the only base b such that d/dx b^x = b^x. every other base induces some multiplicative factor in the derivative, hence why it’s considered the ‘natural’ base for exponentials and logarithms.