Gunk on your edge will certainly affect cutting performance, but stropping is about a lot more than that. There are different reasons to strop:
1. Deburr and refine the edge after sharpening;
2. Bring back performance of a worn (but not completely shot) edge; or
3. Polish edge bevels for aesthetic reasons.
You can absolutely strop back an edge that's been used to, for example, cut up a bunch of cardboard. If you have the right compounds and strops, you can bring back a knife that struggles to slice paper to hair whittling sharp.
Compounds are abrasive. What is the point of using a compound on a strop unless you are specifically trying to convex the edge? A ceramic hone or a stone will do the same job without convexing.
A compound is a way of turning a strop into a sharpening implement.
When it comes to, as you say "Polish edge bevels for aesthetic reasons.", I'm not sure that there is any such thing. The edge is where all the action is. How smooth or coarse it is affects its characteristics. "Aesthetic reasons" don't come into the picture unless you're not using the knife. It's for display only.
Thanks for sharing your thoughts. That goes for everyone else who posted here as well. You've all helped me to think about this subject a little more. I appreciate it.