Even with (compared to BTC nearly static) fiat currencies this would cause a LOT of uproar. Just download a year worth of Forex data and then act as if your USD account displayed its values in EUR instead (or the other way round). Suddenly your balance is different every minute, you cannot tell how much you'll earn and spend any more until you actually do so...
Sukrim, step back and think about it further. If you transfer money from euros or dollars into bitcoin and use it to buy an item off a website in bitcoin then you would be paying more or less in fiat terms by the time you do the purchase. Probably more, with bitcoin rising so much. Are merchants going to revise their Bitcoin prices (usually downward) every minute, hour or even daily?
During the transition period when merchant costs are in fiat, they will be thinking of pricing in fiat terms. It is a hassle to keep revising their prices downwards as bitcoin appreciates. Stale bitcoin prices will always be seen by the public as too expensive.
Making bitcoin a less visible layer underneath a virtual fiat transaction is the way to go. Yes, VF wallets will jump around in value, but if you have $200 worth in fiat and it oscillates between $190 and $210 every now and again, so what? it is not unusable for buying a $10 book.
Finally, someone on this forum is thinking like a user rather than a developer!
Currently, this issue of the value of bitcoins to other fiat is why nobody is spending any bitcoins. I am setting up an ecommerce site at the moment, and am having exactly the problems you are describing. The only solution I can think of is to offer the bitcoin price only once I'm through checkout on the total spent.
If a bitcoin wallet did this automatically, it would make life very easy, and save me 5%+ on Paypal charges. More importantly, my customer would be using bitcoins without having to think about conversion prices etc.
I think we may have stumbled on to something very good here!