OK, so assume $millions of dollars are invested in a Cat 3 installation at PH, plus the expense to upgrade training/crew quals/aircraft status for domestic aircraft to land in Cat 3. This will then mean an aircraft can probably land if it reaches PH to find it below Cat 1 min.
But the problem is reaching PH!
Most B737 aircraft will have to divert anyway, because Cat3 capability does NOT affect alternate minima and these aircraft often can't carry enough fuel for an alternate from the East Coast. So if the
VB aircraft in question couldn't reach PH and hold an alternate (as was the case here, by the sound of it), then it has to divert when the forecast goes below ALTN MIN (regardless of whether there's a Cat1, 2 or 3 capabilty at the destination).
By the way, QF do not always carry an Alternate for Perth. They do have have an internal assessment process however, that sometimes results in alternate fuel being carraied when not required by official forecasts.