Hi Rok - actually, the horn is quite a bit more "nimble" than the trombone. The trombone's slide makes it awkward to play things that are very fast, for instance. The horn has the advantage of the valves, like the trumpet. Even the tuba is technically more "nimble" than the trombone, again because of the valves. However, you are correct when you say that the basic tone of the trombone is more suited to jazz in general than the horn is. And in many jazz styles, the slide is an advantage. Although technically the tenor trombone's range is almost the same as the horn's, in actual practice the horn usually covers quite a bit larger range, and on a smaller mouthpiece, too. This is the reason the horn is considered the most difficult of the brass instruments, and one of the most difficult overall - we have to cover the largest range on the smallest mouthpiece, which means we are using less surface area, and therefore taxing the muscles of the embouchure more.
Getting back to the horn in jazz, you normally see it in big bands, not as a solo instrument. I have occasionally performed with a big band, though mostly that was when I was still a student. There are often big band shows on our pops series, though, I would say at least a couple a season - in fact we have one coming up in a couple of weeks that is mostly the music of Louis Armstrong, I think. I have only given the music a glance so far, as we have a much harder (and brutal on the face) symphonic program to get through this coming week first. Though that Louis Armstrong show looks like it may be pretty brutal, too.
Anyway, there have been a few famous jazz hornists over the years, and there are actually quite a few active right now, maybe more than there have ever been.