Pure cork won't wrap, so they mix cork with other things, and make it most of it ends up being the other things that make it wrappable, formable, and so on. Cork is bark, you know. So "cork bar tape" refers to a category of bar tapes that look like cork and feel corkish, but in fact have quite a little cork in them, but they don't smell like a tree.

What about the cush factor of cork vs cloth?
When the handlebar is high enough, you'll be comfortable grabbing pure steel, because your hands aren't carrying weight. When the bar is too low, even the cushiest tape is like spitting on a camp fire. Cushy cork sells more (in most places) because it scores high marks in the squeeze test, but that's not a good test. Get corkish tapes if you like the diameter or surface feel, but don't expect them to heel your hands.

You can shellac the tan to make it look like leather but it deteriorates pretty fast and gets grody in its own way, so no much different than not-shellacking it. Here's a video that shows how to wrap twine over the ends, so you don't have to use electrical tape.