The diablo, er diabolo, on my 6004 does NOT move with the pivoting gripper mechanism, it is fixed to the tension head which does NOT rock/lock with lockout. Not sure what we are arguing here, just noting a fact.
As such, the gripper must place the same amount of grip whether the diabolo is used or not. it DOES, however, help out with the string angle going into the gripper. Again, just stating a fact.
I use it unless it is inconvenient, which is only occasionally, like when i start my mains.....even then i COULD use it, just don't........or if i'm short on string at the end of M/X.
Also, tension seems to pull the same, with or without. I have checked out of curiosity, just got the machine and thus a diablO last summer. I had never owned a machine with one (a diabOLO) before, only used them a couple times.