I have to give estimates all the time. They're estimates, but they're in the ballpark.

But recently, I had to give an estimate for porting some software to a new environment. I knew it was going to present me with a bunch of obstacles, and I didn't know what the obstacles were, or how long each one would take. I didn't even know how many obstacles there would be.

I didn't want to give an estimate for that. They made me give them one anyway. I did, but I knew that no reliance whatsoever could be placed on the estimate. Whereas other tasks, estimates were close to "bet the company on it" solid.

Also, how did you come to the conclusion that "project management doesn't work" is a historical fact?

Also also, if your teams' estimates are a farce you might consider starting to track time spent on projects and build up a base of real world numbers you can use as guidelines for future estimates. It worked wonders for us.