This approach was rejected by Alexander Hamilton in favor of our current science:
The science of politics, however, like most other sciences, has received great
improvement. The efficacy of various principles is now well understood, which
were either not known at all, or imperfectly known to the ancients. The regular
distribution of power into distinct departments; the introduction of legislative
balances and checks; the institution of courts composed of judges holding their
offices during good behavior; the representation of the people in the
legislature by deputies of their own election: these are wholly new discoveries,
or have made their principal progress towards perfection in modern times.
Hamilton is overstating his case in regards to the ancients being unaware of procedural devices; nevertheless, it is true the emphasis was not on ‘mechanisms’ like Checks and Balances.
After two hundred years though, there have been plenty of events to suggest the classical method should still have a role in political science. Every great crisis (The Revolutionary War, Civil War, and the Great Depression etc) required a great statesman to steer us through it. Even our current dilemmas, Iraq and the Fiscal Crisis, reveal the consequences of poor leadership. A return to study of statesmanship might be in order.