This is not my experience. Companies with strong engineering organizations that are parallel with and equal to the product/business org structure would not have a product management bias. I would only work at a company where engineers are managed by other Engineers who are partners with the product and other business teams, not reporting to them. (I'm a Software Engineer).

I also think that engineers would be paid much better than product managers in such an organization, given the higher demand for engineering skills (there should be more engineers than product managers on any given team) and a smaller pool of potential hires.

I'm not sure this is true, at least in the current climate. At our (Series B) startup, PMs make about half what engineers do.

Not to discount your experience, but at the large enterprises (Amazon, Microsoft, Google, etc.), Program Managers make the same money as Software Developers at equivalent titles. Program Managers are not JIRA monkeys (I love JIRA, by the way), but generally have coded in the past and have a better grip on reality than some MBA candidates.

The tradeoff is this:

1) PMs get broader visibility across the org, which tends to result in faster promotions into management for "good" PMs.

2) PMs atrophy technical skills and become more dependent on the larger organization (they acquire more firm-specific skills in econ talk) than do equivalent developers.

So, sometimes if you like your company and want to advance quicker, you will be willing to trade away some industry or general skills for firm-specific skills to get faster promotions or more power.

I've never worked at a product company per se, but that is exactly why I aspired to transition into project management back when I worked in corporate IT. Can't blame folks for wanting the money and the power after they see how things are for the Vics in their companies.