In every WTL example, CoInitialize is called as the first function of WinMain. I know that WTL is based on ATL, which is closely related to COM, but as I see it, a WTL program can easily not use any COM code (can't it?).
What adds to the confusion is that ATL has classes such as CComCriticalSection, which has nothing to do with COM, despite the name.
So my question is: is it necessary to call CoInitialize in a WTL program, even when no COM is explicitly used?
No, CoInitialize is not a requirement for a WTL application. Many WTL classes are unrelated to COM. Historically, as you mentioned, WTL was tightly connected to ATL, which in turn was a primary framework for COM development, and COM initialization was a natural step because the application was likely to do something with COM anyway.