Cartwheel pennies were not counterfeited often; they were technically difficult to counterfeit (the incused design being harder to create than regular relief design), and the full weight of one avoirdupois ounce per penny made it uneconomical to counterfeit them. So in that sense, it was "mission accomplished", as one of the goals of making the Cartwheels was making a counterfeit-resistant coinage.
However, they were not popular in circulation, primarily due to their weight and size. "Cartwheel" was originally a derogatory nickname applied to them, indicating a public opinion that they were too large and cumbersome for regular use. However, merchants were grateful at being given free standard weights they could use in their shops - it meant they didn't have to go and purchase new one-ounce weights all the time, they could use the coins as weights instead. Some less-than-honest merchants realised that, as people got used to using the coins as weights, they could use heavily worn or even damaged coins, that weighed significantly less than one ounce, as dishonest weights in their shops. It's entirely possible that the worn, damaged, polished example on the right was used and abused in just such a way.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis