If you're a Premier member (I am a Premier Exec), should the ticket agent always mark your checked baggage with the little "PRIORITY" flag, even when traveling in coach?

I've had the bags marked at times, but more often I get nothing, even if I'm flying in upgraded first class. There seems to be no method to the madness. It's like the ticket jackets: sometimes I get a nice gold or silver one, and other times a flimsy blue one, even if I'm in first.

And does the little baggage flag really make a difference? I've had my bag marked first class only to grow a few gray hairs waiting for it to arrive at the carousel.

Just wondering what everyone else thinks ...