That's your problem right there: the subordinacy of engineers.
We are biased to listen to high-status people more than low-status people. The strength of this bias varies from people to people, and from culture to culture. But if you are asking someone to listen to the opinion of a direct subordinate, you are asking for trouble.
This is one reason why Michael O. Church is so big on guilds, or "professions". If instead of being a subordinate, the engineer was a (possibly certified) master craftsman, things would be different. Just picture the manager calling the the engineer "master", then not listen to her opinion.
> […] engineers […] should be trained in how to negotiate with management
Conversely, it's harder to negotiate when you have lower status than the manager. You may feel it is not your place. But if you're a master programmer, offering your services to said manager, then you could feel more confident about talking to him as a peer. You could feel more confident about saying things like "your idea won't work —trust me, it's my speciality."