I found that If I don't do this, the 2x2 is harder to slide into the page's pouch, and once in, the back side of the staple pokes at the page it is in, creating a dent. Worse yet, if you are keeping the 2x2's in a box, the staple could poke at the surface of an adjoining coin, if not flattened. As I mentioned above, I keep my coins in three-ring binders. I store my paper money in inert mylar sleeves. These are readily available in two sizes, small US and large US currency.
Most world currency fits is one of the two sizes.
I do have a couple of bills that are too large for either of these. It is best for the currency you are storing to get these pages in an inert, archival grade, if possible. The short answer to this question is that cleaning coins the wrong way will reduce their value significantly. In order to understand why cleaning a coin reduces its value, you must first understand some of the factors which effect a coin's value. Basically, the less the coin was used, the more value it will have to a collector.