> if you're serious about "building product" [...] You 
  > would build and run something yourself.

Perhaps as a side project, something useful just for yourself. Lots of developers scratch itches they can't scratch at their day job that way; new tech, greenfield ideas instead of maintaining someone else's garbage, etc.

And sometimes those devs go into business for themselves and realize that they don't get to spend all their time building product -- now they've got to build the marketing page and write a bunch of copy and take a ton of screenshots (of features they know they're going to change), and figure out how sales funnels work, and all the other things that go into running a business.

Building and running your own company is the fastest way to get out of pure product development I've ever seen.