Here's an answer counter to the conventional wisdom, which feels a little too self-serving.
What if ideas are things that need to be worked on and hammered out as well? After all, isn't that why working on a startup is more rewarding? The programmer isn't just a programmer anymore, (s)he's also the PM and analyst all rolled into one. Of course, the person in charge has to be good at it all in order for it to work out. Startup people have to "pivot".
I have friends at Apple and Google, and they tell me engineers are encouraged to work on their own ideas. Analysts have shown that those companies have fairly high productivity per worker. One of my closest friends at Apple does all the mockups for her team's features, despite officially being a programmer. It feels as if the role of PM is spread out amongst a number of programmers, who aren't exactly brain-dead with regards to what a polished product should be.
Now in most companies where PM is in charge, it feels as if the toolchain has been optimized to deemphasize the importance and reliance on good programming, hence PM/analyst becoming more proportionally value-dense (whether this is a good approach or not I will not debate).