If that's the way it works, then estimates aren't "estimates." They're "commitments." I don't make solid commitments unless I'm 110% sure I can get what I said done by the time I said it would get done, and I imagine many others don't either. So, the rational response to "estimates
cum commitments" is to only promise what one can deliver with high certainty.
This essentially leads to the same result as when estimates are actually estimates, except that I might feel free to overestimate my capabilities a little, but I'd never want to overcommit at all. In other words, if you just let me estimate instead of commit, you're likely to get more work out of me most of the time.