copper roof above dormer tarnished polishing

Unless you want a lot of maintenance. Most people won't do it, and most people like the normal copper patina process.

Incorrect. You polish the bejeezus out of it, then you seal it with a clear finish to prevent air exposure. Depending on the quality of the sealing material used, it might last 5-10 years between applications.

Properly done, a copper roof can keep its shine for a long time, and never show a hint of either brown (sulphides in the atmosphere are the cause there, if I recall rightly) or green/blue (chlorides, sulfates, and oxides would be the bad guys in this case) or lose the desirable shine.

The critical concept is "done right", which ain't quick, easy, or cheap.

And although it will last for quite a while, it will eventually fail, and you'll be back to a brown/green/blue mess if you don't repeat the process periodically. The huge majority of people don't have the time, money, or motivation to "keep up with it" properly, so the common (mis-)perception is that it simply isn't possible at all, which is patently false.

Personally, I prefer the green/blue weathered look. Just watch out for copper sulphate trying to kill the plants near the downspouts...