No offence intended.
TW was indeed the alternate for a friend's B737 the morning AFTER the
Great Diversion !
They'd added up the fuel and looked at every other diversion option; all were below either ALTN CRIT or landing minima!!
As one of our supervisories said to CASA'a forebears [and they had a few!], "If you stick a long runway with an ILS close to a location with poor forecasting, you can expect MORE diversions here not less!!" [YSCB circa 1974]
You may not have to use the option very often [YPLM comes to mind], but they're still available. Indeed, my friend was almost the second TW diversion.
G'day