I suspect the better reason for making a singleton, then migrating from it is this:

1. By forcing everything to use a singleton, you get to mark every place in the code that accesses a global.
2. In addition, you get to regularize every access of every global, thereby reducing bugs.
3. In addition(!), you start to find the places that were using typo'ed globals.

Now that the accessing is regularized, you can do a global replace for a single global variable at a time, knowing that you have all your globals code still in one place.

Even if you never go past the singleton, it's still a good idea because you have collected all your globals accessing stuff. I did that in a production project at my previous position and it worked just fine. I had one big Exporter module and each package that needed access to a given global structure would import just that one accessor symbol. I could then grep through the code and find which packages accessed which symbols. This resulted in tighter code and caught about half-a-dozen bugs in the process. :-)

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We are the carpenters and bricklayers of the Information Age.

Don't go borrowing trouble. For programmers, this means Worry only about what you need to implement.