Re: "did not include functional specifications"
The classic problem is that you are failing to identify what "somewhere better" means. And it can mean different, even contradictory terms, depending on the business unit. In your example, "somewhere better" for pedestrians means having more crossing points, road traffic be damned. For motorists means a different thing than for pedestrians. What you have in front of you is not a system design problem or an architecture problem, but a plain old politics problem. Same in business. And, let me add, those political battles hardly have a clear winner, and nobody wants to wait for the battle to be settled before starting to build the new system, much more if they can take advantage of some tactical feature or side effect of the new system.
Complex problems have complex solutions, and often what the "best" solution (compromise between the parties) is not found after a few iterations. If you think you can get it right first time, you're doomed even before you start. Except if you're dealing with satellite/space shuttle levels of safety