Agile is about a team and how to make it deliver a product as fast as possible. (that wording can be misinterpreted, but that is for HN audience not PHB)
The key tenet of agile is that people just can't estimate - so sure fine, use magic PM formula - experience, whatever, anything to have a budget approved, but as soon as the real work start, don't bother your developers with it, just get it done ASAP. Agile can help you to estimate better on the long run but not really because of agile directly, but because agile facilitates creating a consistent more uniform development team.
As for developer productivity, at best it will because more apparent who is slacking in a agile team, but if management listen to metric rather than their team lead or the developer themselves all they are measuring is people successful at producing the right metric.
Accountability, that's a corporate issue. When accountability is an issue in a company, it means that somewhere along the line it lost the ability to stay focused on the end product. Your teams are not working together toward the same goal so you need to find "people to blame". Not quite sure how that is related to agile, you do not make people working together by having them stand up everyday 15 minutes with others or fill a whiteboard with stickers.
The problem is that following a methodology like SCRUM, it is possible to produce a shit-ton of metrics, and that's what make managers wet. Those metrics are useful feedback for the team, but if you use it for anything else, you have just recreated the old 90's LOC stupid productivity metrics with fancy looking new terminology.