well, I can't speak at all about chemical engineering, but as a mechanical engineer, I've had all sorts of cool jobs.
I have my PE license, which allows me to be self-employed as a consultant. I've designed all kinds of products and the machinery that makes products. I've also done a lot of manufacturing engineering, process engineering, and industrial engineering. That's where you design the process to make something and optimize it for low cost, high quality, and peak efficiency of the production line. I've designed entirely new factories from the ground up (of course a civil engineer had to design the building to go around it)

I recently begin getting into being an expert witness. That's where you get hired to figure out what happened and how it happened in something like a product failure, an industrial accident, or a car crash. In fact I spent half of yesterday examining a crashed car to figure out the accident sequence.

So, as you see, it's a huge field. I specialize in design, so what I've described is just the tip of the iceberg for mechanical engineering.

if you're interested in mechanical design, I really recommend those shows on cable 'How it's Made' and there's another one also. Most of my career has been conceptualizing the process and designing the equipment like you see on the show. Truth is, I have trouble watching those shows because it gets me all wound up like work.