Now that we have most of core free of shadowing, we can enable the
warning as an error to catch anything that may be remaining and also
eliminate this class of logic bug entirely.
Gets rid of the largest set of mutable global state within the core.
This also paves a way for eliminating usages of GetInstance() on the
System class as a follow-up.
Note that no behavioral changes have been made, and this simply extracts
the functionality into a class. This also has the benefit of making
dependencies on the core timing functionality explicit within the
relevant interfaces.
