Why do you think it needs to be a bank that allows USD/EUR <> BTC?
Because otherwise ordinary people will not have access to BTC and you can't achieve adoption without them.
A Bank has an infrastructure that could make BTC virtually omni-present in the physical world. Any other non-gov institution, would have a hard time setting up an infrastructure in large scale. A bank has also the knowledge to protect herself from bitcoin itself, because (supposedly) understands the financial (and social) ramifications of every choice made AND should be held accountable if things get out of hand.
If UBS (as in the example above) starts accepting BTC transactions, it means that thousands of hundreds of average Joes get instant access to the system. Otherwise, it's just you me and a couple of bleeding edge technophiles.
Firstly, there's a debate on whether BTC is closer to FIAT or to an asset (e.g. Gold).
Let's say we skip that part. Until a world-wide bank like say UBS or a country decides to implement an infrastructure for bitcoin, it won't cut it.
Why a country would want to do that, is beyond me - and probably beyond anyone with a basic understanding of macro-economics - and so we're left with other possible implementations of the protocol.
Until we find a way for average Joe to switch from USD/EUR to BTC and back easily and without fear of money loss, I don't think we'll see any widespread adoption as a payment system.
ps. The argument about using bitcoin in societies where finance is not well evolved, is as ridiculous as it is dangerous. Imagine bitcoin-driven banks in Addis Ababa handing out loans (in bitcoin or the local ETB currency?!) and financial products based on bitcoin. Then imagine that an unknown, early adopter, from the other side of the world decides to withdraw 100.000 bitcoins at once: There you go, you got Ethiopians playing wall-street pranks!