The problem is that Berlin is not just a city, it's a state. The government services outside of the state, like the army or the coast guard, can't just march in and start doing stuff. They have to wait for permission, but the Berlin government took days to announce an emergency and ask for aid.

The private groups didn't need permission. And some, like the police and the firefighters, already had that permission. That is why they were faster, but that is also why the larger and more technical aid took so long to get there.

That was why the Berlin state failed: incompetence. And, apparently, simple laziness and arrogance.