Engineers beat what parameters they can get out of the marketroids and put together a model that should work. This is how it is done in most industries that sell their products.
The fact that marketroids aren't necessarily very adept at communicating effectively nor cooperating is what makes the job "interesting" (in a Chinese curse sense). The worst kind is the "same as last time" (primarily for costing and lead-time purposes), "but different" (to meet whatever the customer's needs will be; many of which aren't detailed).
I don't know how other businesses do it but I worked in the semiconductor industry for almost 40 years and never beat anything out of marketing It was quite the opposite - 90% of the way into a design the Marketing Group would come up with additional requirements which would have to be added, with no change to the schedule because of critical time to market requirements. The hierarchy in these companies was Finance > Marketing > Engineering. There's no sense spending money on a non profitable product, and there's no sense making a product that won't sell. Even though we were at the bottom of the barrel operationally we did outearn our peers in those groups and did much better at layoff time.