Why cruisers outperform battleships as peacetime tools

Did the US Navy send ships to hunt Graf Spee as an enforcement of the Monroe Doctrine?

Not officially; any quiet search was constrained by the chronic shortage of deployable cruisers needed for many other peacetime duties.

No official US Navy hunt for Graf Spee is identified as an enforcement of the Monroe Doctrine, although individual cruisers may have watched quietly. The larger constraint is deployability: a navy can list many cruisers on paper while having very few free for an additional patrol. Limited finances encourage fleets to preserve battleships and destroyers, often leaving too few cruisers for the broadest set of daily missions. Battleships must remain ready for war but can be held back because routine movement consumes large crews and budgets. Cruisers are therefore the scarce peacetime workhorses for presence, observation, and scalable diplomacy.