This is actually achievable in a sane way.

I have done it using the XP planning practices. Basically, you make the suit break everything down into relatively small lumps and place them in priority order. Every week, the team completes a few lumps. Before you do them, engineers grade their relative complexity in arbitrary units. (The smallest substantial thing you do is 1 point; something twice as big is 2 points, and so on.) Every week, you count up the points completed. That's your "velocity".

From there, you let managers do all the estimating they want to. If they want the complexity of a unit of work measured, they ask the engineers. If they want to know when X will be done, they look at the team's recent velocity, what's in the queue before X, and do some basic math.

The nice part about this is the mental judo involved. Whenever they want to know when something will be done, it's their problem to trade features against time. Working like this, it's not geeks vs suits; the suits channel their schedule pressure into productive work: grooming the backlog.