The only reason to use polymer is if you need the L style UIs they discussed at Google I/O.
While Google's really good at Java apis, they're really terrible at JS apis. I love Google, but I would be very hesitant to use their JavaScript libraries or frameworks. A lot of people I've talked to (on irc, es-discus, etc.) don't agree with web components, but Google's pushing it hard.
Web components are poorly based good ideas, and polymer is poorly based on web components, and your app will be (poorly) based on that.
Other people have started posting some of the problems with polymer.
I don't know if it's fair to say an entire organization is good or bad at an individually-attributable skill. The Polymer team wrote the app framework for WebOS. They're not some generic Java guys who got put on a web project. They have a pretty deep background in JS.
I think you're confounding Polymer with Paper. The core Polymer elements that have currently been released make no assumption as to your UI preference, which means you can style them individually as you please.
I've been creating my own Polymer elements for an internal project and have been pleased with the result so far. We've got some particular branding requirements that I've been able to reproduce to great effect. I think as long as you stay away from the messy parts of Polymer (such as making XHR requests in the DOM) then you may find the experience more agreeable.
While Google's really good at Java apis, they're really terrible at JS apis. I love Google, but I would be very hesitant to use their JavaScript libraries or frameworks. A lot of people I've talked to (on irc, es-discus, etc.) don't agree with web components, but Google's pushing it hard.
Web components are poorly based good ideas, and polymer is poorly based on web components, and your app will be (poorly) based on that.
Other people have started posting some of the problems with polymer.