We have that style of "Master-Pattern" and no matter how small a team you have it introduces problems. It's still a hidden dependency, so you don't know if you've forgotten to initialize it before you get an exception. At least for us we ran into the problem that we wanted to make some changes that meant it was no longer a singleton - but now we had to perform a major refactoring.

So you could use a good DI framework such as SimpleInjector and get all the benefits without all the problems. You only have to initialize once, and then it's injected into constructors when needed, and you can inject different implementations depending on context.