One problem of creating your own time abstraction class is not only that you need full control of the code base and introduce everyone new to project to always

One problem of creating your own time abstraction class is not only that you need full control of the code base and introduce everyone new to project to always use this class. Some time-based operations can be quite hard to mock, such as wait for thread synchronization primitive or wait for IO with timeout. However those are most often usually used in the domain where you don't want to mock time because, as you say, there the wall-time and the processing-time is more often dependent on each other and you probably want to test everything exactly as it would run in production.