Singleton as a "one and only one" instance enforcement
This is better handled with standard object construction / destruction; if there should only be one instance of an object in your program, instantiate only one.
If your code would break because more than one object has been instantiated that is a big problem that should be solved.
I mostly agree with what you've said, but in this case I'd point out that the only time I use a singleton is when I inherit this kind of problem from an external library. I actually had that problem crop up in class last semester, where a library we were using abstracted all resources and forced us to refer to everything by assigning it an integer handle. I created a singleton to function as a kind of handle distributor. It contained an internal int that started at 1 (the lowest allowed value for the int handles) and it had a method that would return that and increment it. If there were ever two instances of this class then all of my resources would potentially be invalidated because their handles could suddenly be used to load a new resource. My whole motivation in creating the singleton was to enforce one-and-only-one instance.
That is a poorly designed library, or your understanding of the API might be incomplete.
Such libraries exist where they are just calls to 'getNextResource', virtualizing this across multiple objects can be tricky.
The simplest case of this is C or C++ 'rand()' function, it uses an internal PRN sequence
While not ideal, you could manage this using srand() to set the seed to the known instanced value before a call to the global rand()
Some libraries provide similar functionality, specifying a 'context' or 'device' id for the global functions, which partitions sets of identical resource id's.
If the library had such a feature you could have your 'Singleton' instance, hold and use the device id.
If the library did not support such a thing, time to go bitch them out, they're writing broken code.
Thanks for posting this example, as it is another common reason people turn to singletons, to help shield against code like this.