Controlling the physical space around Congress, the Supreme Court, the federal bureaucracy means that every legislator, judge, and federal worker sees the Guard on their commute.
The message is environmental and atmospheric. Propaganda for the governing class. Power made visible to those for whom there is intent to intimidate.
Extending that, DC notoriously exists as an anomaly violating the foundation that the US was founded on. It is a city that isn't a city, a population with little representation in the federal apparatus that controls it.
DC's legal vulnerability makes it perfect for testing. What works there can be threatened elsewhere. "We did it in Washington" becomes the precedent.
The 30-day limit isn't a constraint. It's a demonstration period.