Back in the 1970s-'80s I veered between thin cosmetic bar tape and that thick foam pipe insulation sold as handlebar padding, before settling on some rubbery stuff that was bright stinkin' yellow and otherwise nearly perfect. No adhesive. It was pliable and tough -- felt about like insulated grips used on some hand tools -- and remained wrapped without excessive stretching. I even reused it after some crashes that scuffed it up. Cleaned up using pretty much the same stuff I used to clean my car -- including Armor All. As I recall it was mid-priced, cheaper than leather.

I recall seeing it's still available somewhere but can't find the bookmark at the moment. Not sure if it comes in colors other than hi-vis yellow.