Set aside show/pretty/ugly/weight, wrapping with thermal wrap can compromise SS ?
http://www.centuryperformance.com/exhaust-header-heat-wraps-do-not-use.html
I laughed so hard reading that link my ass caught fire.
Let me summarize it for you
1. Exhaust wrap is effective at keeping heat in, more so than ceramic coating wish it ever can. Cool, no sites ever disputed that fact.
2. The site you linked to, Century performance sells Sanderson headers.. which guess what? Offers ceramic coating on their headers for a premium of $200 and up. The guy selling snake oil will say snake oil is good and Indian oil is bad, and vice versa.
3. People who parrot saying headers will fail due to wrap.. never wrapped theirs before... people who did, well...
https://forums.nasioc.com/forums/showthread.php?t=498224
wrapped my stainless steel header 7 years ago.. guess what? It's still in one solid piece. Car is daily driven everyday. Just recently wrapped my downpipe... better check it for cracks cause it's crap quality. But I have absolute confidence in the header.
4. Headers do fail even without exhaust wrap, that's call thermal fatigue, but you can also call it CRAP headers. They can be crap due to weak design, high vibrations (especially), being stressed beyond designed capacity/load.
Example:
http://www.s2ki.com/forums/s2000-forced-induction-142/exhaust-manifold-crack-record-thread-959149/
5. Saying thermal wrap causes rust and thermal failure on stainless steel is like saying oxygen causes rust and we shouldn't breathe...
The reason why i avoid wrapping is exactly what sweelt shown you above. I hope you respect different opinions and no i'm not the kind of guy that cares about "show and not go". peace.
People who hang out here long enough knows I'm not here to be a popular guy, I generally don't give a shit what people say or do. But quoting half truths like the Bible is a no joy for me.
So if you BELIEVE that thermal wrap is the cause of cracked headers, I've thrown that claim out of the window cause they crack without wraps too. Sure you can still believe that, but you better stop breathing cause oxygen causes rust dude.
I respect science and truth. Not opinions cause those are like assholes, everybody's got one. I've shown that your "reason" is invalid. And that link is written with commercial interest in mind. Guess what? I'm not selling anything.
And to answer your original question, give Brasso a try. But if it's etched in with oil I think it's pretty challengeing to remove, which is why I suggested wrap in the first place - that way you won't look at the eye sore and get a cooler engine bay at the same time. Black wrap looks damn cool on headers.