Putter over-grip? | Golf Monthly

Having mooched around the golf shops for sale stuff, I've noticed that I picked up quite a few putters with a thicker wrap-around type of grip, similar to a tennis racket. I have to say this type of "fat" grip feels good in the hands.

I was wondering if there is any reason to not use tennis grip tape and wrap it around one or two of my putter collection and try it out. I have 3 rolls of tape and thought I might accessorise one or two for fun. Can't see they'd be illegal and it might even make the grips on one or two a bit better in the wet.

Would using a sticky rubber tape over the top ruin the factory grip for future use? and could there be any logical benefit given I liked the feel of the few I tried?

Or is it a daft idea?