Only benefit I can see is if triple tree stand rubs the fairings. Ours puts pressure on the SV's fairing, so I only use it on the SV for major work. In my case, if I just needed to pull the front wheel off, probably easier to use the fork stand.
If it didn't rub, I'd always use the triple tree stand. Probably just a bad design; my setup is cheap.
'96 DR650, '01 SV650, '10 Aprilia Tuono 1000R