Your entire argument is premised on the notion that singleton is something else entirely. You even say "What you probably wanted was a simple single instance of a class instead of a Singleton".

Ummm, for most people, those things are one and the same. Are you asserting that the meaning has changed over time and that people are calling things singletons that aren't really singletons? That might be a valid argument, and an interesting one. Are you saying that enforced uniqueness of instantiation in a a class is in some ways "ugly" and almost kludgy? That is probably true (but of course a matter of taste) and would make for good discussion. Are you saying that there are "cleaner" ways of achieving singleton benefits without enforcing their unique instantiation? That also would be interesting to read about.

But to assert that a singleton is something other than "a single instance of a class" means that you fundamentally misunderstand the concept of the singleton.