[andos]

for example, you only want one piece of code drawing directly to the screen

therein lies the problem: most of us are, in general, terrible at predicting the future. By the time I notice I now want more than one piece of code drawing directly to the screen, my code is already full of wrong assumptions.

One way of easing this is -- as you point out -- to make dependencies explicit and abandon GetInstance. Better yet if realizing that, as a design guideline, "needing only one of something" trumps "something being a singleton" any day. This is the kind of future-proofing that generally doesn't hurt the schedule.