"As a product manager, your job is to live in the problem space. You should spend nearly all of your time focusing on your target customer, what needs they have, and what value you are going to provide to them. Nobody else in your organization is set up to spend time in the problem space like you are."

Couldn't agree more. I would add it's the PM's responsibility to bridge the gap between the Solution and Problem spaces, especially when compromises need to be made at implementation time.