Chosen Solution

I am replacing the battery in a late 2013 MBP Retina 13”. Getting the battery unglued was a royal PITA. Is there any reason not to leave the new battery unglued, i.e. to leave the cover paper in place? Is the glue really necessary?

The problem with the rMBP chassis is there are no screw points, so you cannot bypass the double sided tape method sadly. You can probably replace it with weaker tape that comes up easier, but the thickness has to be exact or very close - as in a few mm thinner at most. The problem is taking the factory tape off of the battery is a high risk procedure as well.