Now there's a flaw in our economy that's waiting to be exploited. Handling fees that are higher than the amount received, effectively draining the company of cash.
It would also drain resources and create massive amounts of paperwork. Even though the process may be mostly automated I'd hate to revise those books, assuming enough people had done this.
Kind of like a distributed denial of service attack.
Of course it's easily remedied by blocking all cash transfers under a certain amount. I guess you're not obliged to accept money, but still it'd cause some extra work. Probably not enough to bring any given company down, but an interesting thought nonetheless.