I take mine off although the current barbel rod I have still has it on 16 years after it was made, will be removing it though.
Take it off, if you change your mind it's pretty easy to buy a roll of shrink wrap tubing and reapply with a hairdryer. Can even use different colours.
Never been able to understand why anyone would pay good money for a cork handled rod and leave the plastic on, The joy of cork is the tactile feel of it in your hand. Easy enough to clean with warm soapy water and a nail brush.
Just took mine off, it's the only rod that I have ever left it on, you can see where water has got inside the plastic and slightly stained the cork,doesn't matter, my grubby hands will even that out, my mate always leaves his on even with mould creeping up the inside of the plastic, can't be good for the cork.
Why would you leave the shrinkwrap on ?? Cork is expensive. If you want to hold plastic then don't pay for cork get 'horrible' EVA or very cheap 'laminated' cork sheet etc. Cork has a better 'feel' or grip.