Does maximum velocity mean maximum productivity?
Absolutely not. In an attempt to maximize velocity, a team may in fact achieve the opposite. If asked to maximize velocity, a team may skimp on unit or acceptance testing, reduce customer collaboration, skip fixing bugs, minimize refactoring, or many other key benefits of the various Agile development practices. While potentially offering short-term improvement (if you can call it that), there will be a negative long-term impact. The goal is not maximized velocity, but rather optimal velocity over time, which takes into account many factors including the quality of the end product.