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We can sort quicklaunch items directly on a website or with powershell (see a great tutorial here).
But is there an option to tell SharePoint:AspMenu in masterpage to automatically sort the quicklaunch items?
Modifying the masterpage for each site collection is going to be significantly more work than configuring this the appropriate way. This is the kind of setting where the powershell script you reference makes the most sense.
There is an option directly in the UI under Site Settings - Navigation - Sorting to automatically sort the list of links.
Required, but never shown