As I mentioned before, CX had to "communicate" for years with ASA in order to be able to use 16L/34R, CX were only recently granted permission to use it. ASA have different internal rules for international carriers than they do for domestic.
I find that a little hard to believe given that I have seen QF and foreign B744 arrive and depart on 16L/34R.
In YSSY it is NOTAMed that 330/787 can be processed onto 16L. If you want to hold for 16R and fit in thats fine, but you should not be cutting in on some other guy who now gets sent over to 16L just because youre not comfortable landing on a 2000m+ runway.
It remains though that some Asian airlines in particular flatly refuse to land on 16L/34R which is basically giving themselves a competitive advantage even though their aircraft is more than able to handle it.
(a 737/A320 doesn’t qualify as anything more than a light twin)
Except the braking action in your 'heavy' is actually better than my light twin so maybe we should start requiring 16R and 34 in YMML all the time.