I've also worked in consulting and appreciate the explicit requirements, but I find the formality much less efficient than the process you describe earlier. It ends up being very "waterfall" and exactly the approach the Agile Manifesto attempts to counter.
Perhaps you prefer a more waterfall, hierarchical development process, or the companies (big ones) or industries (highly regulated) that necessitate it?
A week-10 day sprint on _one feature_? They haven't drunk the scrum kool-aid yet. Just wait until they do - then every feature will be a "story", and no individual story will be allowed to be assigned more than 8 "story points" (which for some reason means "one day"). If you think a "story" will take more than 8 "story points", you'll be asked to break it down into "subtasks" of no more than 8 "story points" each (you'll be asked to do this accurately in a few minutes in a standup meeting). Trust me, if you tell a higher-up non-programmer that there's anything wrong with the development model, they'll hear "we need to move to the 'scrum' everything-is-mandated-to-take-less-than-a-day development model".