Suppose getting a good engineer would contribute $2 million / year profit to a company. That company would offer a higher salary than the going market rate, and thus steal engineers from competing employers (in fact, that's exactly what FB, Google, LinkedIn, etc. do: you can ask them to match or beat the other company's offer). Since regardless of how badly engineers negotiate, they would still be attracted by a higher offer. Then other companies would also offer higher salaries, to avoid missing out in hiring. This cycle won't stop until compensation gets to a good fraction of that $2m/year; say, $500-800k/year or so, leaving room for overhead (office rental, benefits, etc.) and profits. The fact that it doesn't happen tells me that me that most engineers probably aren't worth $2m/year to companies.

I do agree with your last point: engineers are often idealists and/or they have very strong preferences about what they want / don't want to work on. So they may often be willing to give up much better comp in order to satisfy such preferences. That's why startups get away with paying maybe half of what large corporations pay. Still that's not nearly enough to explain the gap between engineer and executive compensation.