Well first, the big problem is they make promises based off of the estimates we give them, which they then cut down and over promise. It's a careful dance between giving yourself the padding you need for if something goes wrong, and not letting them think they can cut down on that necessary padding if they find out you didn't use it.

For us, we under promise and over deliver... Sales over promise, and project managers bid as low as they can to win contracts, and panic when the numbers aren't working because they cut it too close or didn't push back/renegotiate scope creep

So then, when the numbers don't work and their boss tells them to fix it, they go to their team and tell them to make it work. And the only thing they can do is set meetings, make demands, and yell... Sure, you can tell them to go fuck themselves, but at that point you all look bad - if the technical and functional chains of command aren't separated (more common), they just point at you as the problem to whoever signs your paychecks... Since talking to that person is part of their week and you're busy working, that's probably not a fight you'll win.

If they're any good, they do exactly what you said - they come over, say "hey, I've got this problem... This guy wants this, what will it do to our timeline?" And, by being proactive and trusting the experts, they can just go back to the customer and say "sorry, we went over the numbers and it blows out the budget, these are our options based on my expert and the contract vehicle"

Unfortunately, most people aren't that good at their jobs. A lot of project managers have an ego and like to do handshake deals... once they start agreeing to things on their own, they put the whole team in a no-win situation