I've recently started playing the trombone for fun (read: I'm not taking lessons). I've noticed when watching many trombonists on video and in pictures that they often put their index finger over the top of the mouthpiece while playing.
I've tried this myself to see if it had any affect on my playing, and I only noticed that it made it harder to hold up the instrument for me.
Is there any benefit to this finger placement? What is the purpose?
This is only for comfort. The part where you hold the trombone is not very ergonomical so we search for as comfortable position as possible, with control of the instrument. Try various hand positions yourself to see which works best for you. Ideally you should not lift you left shoulder at all (do check in a mirror, lifting left shoulder will with time lead to a lot of pain), the full weight and control should be in your left hand and the slide should not support the trombone weight and it should slide totally freely. (Ideals are one thing, reality a different). Whatever works for you.
I used to play the bass trombone and had a 2+2 hand positioning: 2 fingers in front of the bar and two behind. Index finger on the mouthpiece. This made the movement of the two valves controlled by left hand more free as well as getting a better balance.
There are varius devices available that improve the ergonomics. Some are extra support bars mounted on the instrument.
I just asked a trombonist; the answer was, that it is a convenient place to press against, so the instrument does not tilt, since it requires less effort than more forceful grip.
Some players do this to avoid using too much pressure. Paul Tanner was a prime example.
