The difficult part of being a good PM in a team is that Agile is hard to do right with real humans. Even if it can be reduced to the Agile Manifesto, putting it in practice is difficult and takes work, time, and skill. The ability to consistently create good practices are what differentiates the good from bad PMs.

So while I agree with you that it does reduce to the Agile Manifesto, I'd also say that from a PM's perspective, that's not the point.