Better suited for discouraging scraping. 2 cents * 300 scrapes = $6 although 2 cents is huge over estimation and you would probably not show this every time. Only when there is unusual traffic.
If it actually cost 2 cents, it'd be tremendously useful. There are huge tranches of abuse that would become unviable with that resource cost.
In reality passing the PoW will cost more like 1/10000th of a cent, and you can't make it cost significantly more (let alone 2 cents) without making access totally impractical for real users. Proof of work challenges for abuse are basically snakeoil, it's impossible to make the economics work.