I think it is considered an anti-pattern because a Singleton class can't be instantiated in a normal way by other object (except by calling such method commonly named "getInstance"). So, it will look like the class is being used directly without instantiating it to create a usable object first.
I agree with you that Singleton can serve as a global unique instance. I learned from some people that as alternatives for Singleton, we can use static and/or final variables, and we can also use enumeration (so that we can group multiple variables under one group name as what we usually do when we are working using a normal class/object).
However, these alternatives can only match the capability of a Singleton class in storing states/values. If we need unique functions to work with, those static/final variables and enumerations cannot help. In my opinion, this is the case when we need to use a Singleton class (when we need some unique functions to work with static/final states/values).
Cheers... :))
