Put it this way.
Take a point 150nm from the R/W. Aircraft at FL390, if allowed to descend normally will maintain that level for around another 30nm and then descend at idle thrust until the approach. If the approach is going to be delayed, then fuel is required for the hold.
If you request a min speed descent, then the descent point moves further away, so the aircraft may descend 150nm from the field (at idle thrust the whole time), saving 30nm at cruise thrust and maybe avoiding a future hold - The crew does need to be advised early though!
so case a) Extra 30nm at cruise thrust and fuel for holding.
case b) Engines at idle the whole time.
No brainer!
Oh and I've been known to descend from that level at 220kt the whole way - A light aircraft helped! Just discuss with the crew what is possible because a whole load of factors can come into play. The other tactic can be to ask the crew to arrive at a waypoint at a time...