We filed an alternate on every single flight. Typically Batam for Singapore, occasionally KL. But whether your fuel policy requires you to carry an alternate (SQ, CX etc) or holding fuel in lieu (Aus carriers), the trick is knowing when to give it away and divert.
That 3rd set of eyes on the flight deck might have helped, but he/she may not have been technically allowed there due being burned out and therefore required to rest in the cabin. I know nothing about Singapore FTL’s, but have operated under such requirements numerous times.
Interesting report.