I tend to declare as static all the methods in a class when that class doesn't require to keep track of internal states. For example, if I need to transform A into B and don't rely on some internal state C that may vary, I create a static transform. If there is an internal state C that I want to be able to adjust, then I add a constructor to set C and don't use a static transform.
I read various recommendations (including on StackOverflow) NOT to overuse static methods but I still fail to understand what it wrong with the rule of thumb above.
Is that a reasonable approach or not?
There are two kinds of common static methods:
There are a few common uses of "unsafe" statics -- for example, in the Singleton pattern -- but be aware that despite any pretty names you call them, you're just mutating global variables. Think carefully before using unsafe statics.