You know me, Mr. Ride What You Like. If they feel good, use 'em, with or without cotton tape over them, and the hell with the rest of us.

As to the original question: Grab-Ons are certainly "vintage," but whether they are "classic" is open to debate.

Another possible option for your consideration is multiple layers of tape. A layer of a nice padded tape with cloth over (or even under) it gives some extra padding. I've done that before and it works pretty well.

On a different but related note, it is possible that your bars are too low and/or too far forward for your maximum comfort. (we are not as flexible as we use to be). More often than not, if you are correctly positioned on the bike, padding on the bars or in gloves is not really necessary. Not always, but it is more often than not.