Qantas has to install infrastructure is so many geographical ports, due to end-of-line operations. That means kitchen in each port, fleet presentation in each port. Engineering in each port etc
Singapore doesn't. It has it in one port - Singapore. All other ports are subcontracted via very aggressive tenders, driving absolute benefit in unit cost to Singapore airlines.
QF cannot do the same because?
In fairness for this part of the argument, I believe QF subcontract their catering/ground staff etc in Singapore to SATS -- which is owned by Singapore Airlines. There is no such catering truck sitting around SIN all day waiting for QF to arrive. Surely this is indicative of other stations around the world??
On the other hand, QF used to do the lions share of foreign airline ground handling in Australia until the past few years when anecdotally contracts were given away by management jacking up prices by 50+%.