It can add to particular grooves.
A good example is Larry Mullen Jr on U2's mega hit "Pride (In the Name of Love)" where Larry plays the left side floor tom one 16th note after the snare. It would be really awkward to play that groove with the traditional left side floor on unless you played the entire song left hand lead (which is possible, but would likely affect the feel).
I lifted the same concept on this song:
https://www.youtube.com/watch?v=wwddaJ8Uk4g
Larry also used the left side floor on U2's hit "Desire" by playing the Bo Diddley beat divided between the floor tom on this left side and the floor tom on this right side. Could he play the same notes without the left side floor tom? Sure, but the song would feel different.
Pete Parada (now with the Offsping) played on an album by a band called "Engine" some years back. There was one little fill that set up the chorus on a particular song. It was subtle but pretty cool. I worked out the fill with the floor tom in the traditional position, and while it was the same notes, it didn't feel the same and sounded awkward instead of cool. I looked inside the CD cover at the liner notes, and there was picture of Pete in the studio with a 2nd floor tom on the left side. So I moved a floor tom to that position, and suddenly the same fill felt right and sounded cool. The notes were technically the same, but the feel completely changed by moving the floor tom.
That said, except for that one song, I don't find enough of use for a left side floor tom to keep one there.