well,
I never had them on my Plymouth and I was pulled over all the time (because the local PD are apparently not trained very well and have no idea what classic registration looks like....('69 tags) I was never hassled for my lack of windshield wipers or side mirrors, or marker lights or door handles, the only thing they didnt like was again, my lack of a windshield registration sticker. For what its worth, the inspection station I was using at the time admitted to it being a problem, but overlooked it for five years.
there are thousands of shaved rods in H-town, they are driven infrequently and rarely get pulled over and ticketed. Most officers are very understanding when it comes to custom classic/vintage cars. form over function. they really only have a problem when your daily driver accord or SUV doesn't have its side mirrors.
but in my opinion there are so many fantastic mirrors available in the aftermarket its silly not to have atleast one. you can attach them to the drip rail, or even get those little stubby aero mirrors that I see used on some of the JDM rides.