Article says they would make cuts in the coins to tell if they were counterfeit and that "greatly reduces their value to collectors" but wouldn't that be cool to have an ancient cut and verified coin? 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.
These things don't have intrinsic value. They're worth what collectors think they're worth. I'd be happy if I'm interested in collecting something that is unpopular/inexpensive. Now, if anyone really cares, like if someone has their own hoard of defaced genuine coins, they can try to hype them up in normal ways, write editorials in trade mags, talk at coin shows, or, most likely get numismatics influencers to hype them up, etc.
The ancient tests didn't just chop into the edges like the article mentioned, but cut gashes into Athena's face, into the owl, and often both with several severe gashes marring the coin, significantly reducing their value as an ancient art object.
Some people collect things like that.