So each spam message will take an extra second and 2 additional cents for electricity? I'm not sure what's the use case here.
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.