> Seems they would be more rare and more valuable.

They are not. There are many, many, many cut coins, and often the cuts are "disfiguring" which will typically harm the "eye appeal" of the coin.

Cutting coins was common practice of the time, and if a coin passed through many different hands, it was basically inevitable it would end up cut.

It's kind of like seeing writing on cash... Most people don't write on their money, but enough people handle it that it's going to happen.

The most valuable coins typically sat in hoards, uncirculated, since circulation would itself wear on the coin and reduce the grade. I agree that seems a little backward, since it's not nearly as interesting to imagine the "life" of a pristine coin, but it is what it is.