Singletons get a bad rap from programmers. Just go do a search for "singleton problem" and read any of the first 100 results. From all the anger you'd think they cause disease, or burn books, but no. They're globals, and programmers hate globals.
The recommended "solution" to the singleton problem is to pass the potential singleton to every class that needs it as a parameter so that you can see it is used in the declaration for the class. It's only one variable, or one parameter to a function call, so what? That's the approach I took for my entity system, dutifully passing it to every class that needed it, and having them store it internally if needed.
The problem that developed is that the ES is the central database of my game and it is used by dozens of different modules. Over time, the standard approach had amounted to a few ugly workarounds, hundreds of lines of code to maintain, tens of thousands of instances of one variable, and hundreds of thousands of function call parameters - every frame.
I'm extremely pragmatic and I've always taken other programmer's grand pronouncements on code purity with a large grain of salt. That was clearly an unacceptable trade-off just to avoid a global. Singletons are tools, use them appropriately.