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.
Places all of the timing-related functionality under the existing Core
namespace to keep things consistent, rather than having the timing
utilities sitting in its own completely separate namespace.
