Remember: Agile does *not* equal fast.
The fastest vehicle on earth - space rockets - require the most exacting work and management to avoid literally blowing up.
A bicycle is more agile and precisely because it goes slow enough that it can make a hard turn without ripping itself apart.
Is your software project a rocket or a bicycle? Which would you rather be on when something goes wrong?
@jcholder I think you meant "high forward velocity". Because the example you gave is a fast turn. There is definitely a notion of "fast" that comes with agile. ;)