Why should I request a long landing?
There's no mention that I can find of "landing long" ("landing deep" is sometimes used outside the US) in the FAA's P/CG, AIM or ATC procedures. So it's fairly safe to say that it's an unofficial instruction (assuming I didn't miss it somewhere).

The main reason for doing it is to avoid a long taxi after landing, but I suppose there could be other reasons too, like coming in too high on a long runway or avoiding wake turbulence. The point of requesting it - and not just doing it - is that it may mess up sequencing at a busy airport because you take more time to clear the runway, with the result that the tower has to instruct the aircraft following you to go around. As my first instructor said, "once you're cleared to land it's your runway".

I've never been asked by ATC to do it but I have been asked by the tower to "land short", to minimize my time on the runway and let an airline flight take off ASAP. However, it was clearly phrased as an informal request, not an instruction; something like this:


  N12345 Clear to land 36L, appreciate a short landing if you can manage it


So I think the conclusion is that landing "short" or "long" is simply an informal way for pilots and ATC to make things work a bit more smoothly.