I can see this working if you put in one piece of tape and never need to touch it the rest of the time, but I put tape in and out, as my thumb is shrunken in the cold weather and swells as I bowl and warm up.
It also doesn't work if you're layering tape and need to put one piece just barely below the next piece. The paper backing blocks your vision of where the previous layer ends. PLUS you can't use the paper to remove the tape; you need another device.
I use a 1/8" wide flat bladed screwdriver about 4" long to both install and remove tape and install and remove shims from the back of finger inserts. It much easier to use for all these purposes and much easier to see when layering the tape.