As a package author you use whatever you want (rollup, webpack, gulp, grunt, ...), but you will most likely publish to npm, because bower is dead.
As a consumer you use npm or yarn, it doesn't matter, and a tool that handles modules, probably webpack. Even if you'd use something else (rollup & parcel come to mind), it doesn't matter, they will all treat your dependency the same.
EDIT: Yeah i just saw you're referring to Polymer. I take it back, everything you said applies. But then again, people probably want to suffer when they use it. Though very few actually do use it. I just don't think it's a good example to make to describe web dev in general. Rather Google was the only one that missed the train it seems, they worked in the opposite direction.
Polymer starter kit
https://github.com/Polymer/polymer-starter-kit
- npm
- bower
- polymer-cli
Doing a polymer test requires downloading and installing Web Component Tester, which then requires:
- npm
- grunt
- gulp
- bower
My relatively standard project (using React) needs just Yarn and Webpack. It's got quite some dependencies, but I've never run into those being insufficient.