Banks become forced to compete with an (almost) free and instantaneous method of transferring value (sending bitcoin peer-to-peer without the use of a third party).
It currently costs $40+ for a comparable fiat service (wire transfers).
True, but there's a decent case to be made that (1) transaction fees will have to increase (in general) as the block reward decreases, and (2) transaction fees will have to increase (for these centralized services) if they want to eat the cost of fraud [1].
Without the use of a third party? Bitcoin transactions need to be confirmed in the blockchain which requires third-party miners to exist. Mining costs are relatively high considering the value provided. The blockchain is not at all (and was never intended to be) an efficient way to transfer digital funds. It was created to be decentralized and it serves that purpose, but using it to back a centralized system would be self-defeating, hence this comment thread.
Transferring value in the form of maintaining electronic accounts isn't comparable to wire transfers of fiat where the funds are made available in local currency. Banks don't just track numbers in accounts: providing liquidity and ensuring those numbers actually mean something is not trivial. If bitcoins were globally accepted it would be a more competitive service, but even then there would be the issues of fraud protection and compliance with money laundering legislation that bitcoin doesn't handle well.
"Rest of the world" is a bit of an overstatement, and even then it's only within certain zones. Inter-zone transfer on the global level is still slow and costly, where ever you are.