Is there a coin or exchange out there that's dedicated to doing something with "dust"? If there were a coin/exchange out there that could sweep up all that dust and turn it into its own coin I feel like it'd be extremely popular. Just imagine all those zero's in your account that are actually zero and not 0.0324?!
Dust- To put it simply, the remaining small balance left in your exchange after a transaction.
Conceptually, and by the way you described it, that is actually a great idea. With all these coins today the amount of "dust" would probably amount to something significant. However, the problem is that technically, a coin like this would be hard pressed in development. The coin would need access to multiple blockchains and would have to go through very secure security and penetration testing. It would be a nightmare to develop.