If you don't understand the role of product design in making a successful product (and the difficulty involved in making correct product design decisions), that speaks only to your own inexperience.
A "product designer" is someone who got daddy to fund their "gentleman's Cs" MBA degree and then posts online saying they have a brilliant idea for a company and they just need to find some programmer to implement their grand "Facebook for Dogs" idea and they'll graciously give them 20%. Someone who idolizes Steve Jobs and whose eyes glaze over when any of the actual fractal complexity of the world is presented to them.
The gap between "high level goal" and "features to implement" is just as complex and squirrelly as the gap between "features to implement" and "lines of code".
If one side gets too much power then it can land in situations like you describe (design makes unrealistic requests, or engineering over constraints the product). When the balance is right then working becomes quite amazing, nothing better than seeing my work (engineering) used to make stuff I couldn't even think of and I can see the appreciation of helping design make their vision come true.
"SOMEONE has to solve The Door Problem, and that someone is a designer." -- it sounds like literally thirty minutes of work per week. Just admit that your job is easy and cushy and the programmers and artists are the only ones doing any actual work. They make fun of you when you're not in the room. They add ducks to animations just so that you can feel important by telling them to take them out. You're a parasitic drain on the project, not a "big idea man". Everyone already knew whether or not that door should lock before you were asked.