Programs like this won't stay secret anyway - somebody is going to see a test flight in the distance, or an employee at a contractor will leak.

Announcing it gives the military a chance to control the narrative. If a photographer snaps a test flight and it appears on Gizmodo with the headline "Military testing secret drone swarms to kill us all", there'll be a massive public outcry, a huge negative PR cycle, possible a Congressional inquiry, and in the course of doing damage control the military will have to reveal more secrets than if they just announced the project in the first place.

Americans are not shy about inventing details when they have none, and also have a tendency not to trust either their government or the press.

Advertising, given huge income from arms sales. Also perhaps generating fear and awe.

It's definitely a form of advertising. US companies often publish vast amounts of public R&D, and universities routinely do it. The US military sometimes behaves that way for the exact same reason.

When you can advertise that you're cutting edge, it helps attract the best minds. That's dramatically more valuable than worrying about eg China or Russia stealing the idea to Gremlins. Those ideas and technologies get out regardless, you can't protect them very long. Competitors and adversaries are going to catch up with a given piece of technology, even if they have to figure out how you did it the hard way. By recruiting the best minds to work on problems, you can ensure that you remain a lap ahead of the competitors that will steal or copy from you regardless. If something is very sensitive, then perhaps you can buy a bit more time by keeping it strictly secret, it's still going to get out. If your tech is good enough, powerful countries will do anything to get at it.

Good point! Advertising for "the best minds". One of my math professors was almost an NSA recruiter ;) I was never good enough to get the pitch, however :( I found engineering math to be much more useful.

vis. Google's open source offerings.

And even Microsoft's ;)

During the Cold War we had two government bunkers that only a handful of people knew about in my country.

30 years after the Cold War when Russia opened their soviet archives, it turned out that they were never secret at all.