There is value to other First / Business pax who get better service for crew when the cabin in not full. Every wonder why US airlines are always full and all the pax just criticise their service. Crew may be less rushed off their feet and deliver better service (like top-ups of warm nuts) if the F cabin was not always full.
SQ is one of the profitable airlines in the world. They do not upgrade unless they really have to, like when they are overbooked in Y but not in J or F. So cheap upgrades are not necessarily the route to more profit/revenue. You do not devalue the F product.
SQ makes pax pay a premium to fly in their new F and C seats - and such is the hype of the service and product - people do! SQ does not even give out amenity kits to C pax without any drop in loads.
CX, another airline that pax rave over, also do not regularly upgrade.
I have seen SQ F when the cabin is full. Service levels do drop substantially.
On the other hand, I have been in MH F all on my own with three crew members to service me. I have also been in CX F and SQ F where there were only a compliment of 4 pax. It makes you realised why premium pax are will to pay top dollar for that kind of service. We constantly talk about that WOW factor and being made to feel special when flying FIRST. This is not going to happen if you allow a hand full of chavs upgrading at the last minute.
Proof
While airlines allow top tier FF to upgrade at the gate? How close are they to filing Chapter 11? Compare that to SQ, CX or BA that do not allow top tier FF to upgrade (unless you are BA Prem, of course).