Why would you? I’ve never been a fan of adopting technology for technology’s sake without a problem that you’re trying to solve with it. (n.b. that problem could acceptably be ‘I want to learn more about this technology’)
1) If Web Components work as-advertised, we'll be able to build our own primitives for the first time in the history of the web stack; no more shoehorning rich Internet apps into a framework that was designed for academics to share term papers. This is both fantastic and a fundamental shift in the way apps are written.
2) You can make web apps that look and feel native (on Android) for free.
Sorry, I phrased my original post badly. That wasn’t a rhetorical question, it was posed to the OP. They didn’t give any reasoning as to why they wanted to adopt Polymer, just a blanket ‘should I?’. Your reasons are both valid though.