I cannot say if they will damage the pockets or not 100% however you are creating outward force on the bond between the rubber and the rail wood. If left in long enough and the spring is strong enough it could in theory separate the rubber from the wood.
I also like most others here, do not recommend these because, although it does reduce the size of the pockets, and you are correct it makes you try to control it more, it also is very discouraging to miss shots all the time and gets in most people's heads. Even strong players. Especially as much as these reduce the pocket and the unnatural rejections because of the raw rubber.
Might I suggest a safer better solution. Make your own. I made a set years ago out of that flooring stuff you see in kids rooms or shops that interlock together. It was a half inch thick and it reduced the pocket by an inch which is still a substantial reduction but not so much that it is counter productive. Because the material is firm but not hard it acted almost identical to a real real and nipples and did not "grab" the ball like the spring loaded ones do. It acts way more natural and feels real.
Here is kind of a tutorial on how to make them but it isn't rocket science:
http://pool.potatooo.com/making-pocket-reducers/
And this is the kinds of material I used but I think I made all six out of one OR one and a half tiles. So with a six pack you can make like for or more sets. I made a set for me then a bunch of sets for others and sold them for just enough to cover the cost of the material and then I got my set for free:
https://www.walmart.com/ip/Stalwart-6-Pack-Interlocking-EVA-Foam-Floor-Mats-24x24x0.375/51042649
Just a quick hint though. I made mine then heated them up a little and put them in place and taped them exactly where I wanted them let them cool over night. When I woke up I took the tape off and it was like they were molded into the pocket. Even if I took them out and put them back in they pretty much fit like a glove
This is by far a more superior way to do it. Once formed they pretty much stay in place. They are extremely easy to put in and take out but can be left in four long periods of time as well. There is no outward force like with the spring loaded ones. You get a substantial reduction in size but still feels natural to play. When you hit them going into the pocket it reacts way more like the way the table naturally would instead of giving you a unnatural roll. You still have to play a tighter game and forces you to play better but doesn't discourage you as much because your not missing as many shots that would have went in of the nipple but where rejected by the raw rubber of the spring loaded ones. It's just a better experience all the way around.
I hope this helps you and I hope it works out for you'd in any case good luck.
