I hope you have better experiences with product orgs in the future, because based on what you're saying, you have worked with some really bad ones.
Requirements gathering is the main job of the PM, and it's most definitely not technical (or at least not remotely to the level of technical knowledge required to actually write code).
For example, a PM at Twitter defined that Tweets should be 140 characters (at least in the olden days). That's a fundamental requirement of the platform, but it's related to the company's objectives, user engagement and other things that have nothing to do with writing the code. There's zero reason that engineers should have anything to do with that. Once it's been decided that Tweets are 140 characters max, then that requirement gets handed off to the engineers to actually do the development.
Obviously all oversimplified, but the point is that if you think requirements are technical, then you're probably dealing with bad PMs who aren't drawing them up particularly well. The irony is that when this comes up, it's usually because the PMs used to be engineers and don't have the experience to separate the two roles.