Good point. But how would you decide the value? Would that be up to each individual trader or what? Clearly this will not work in a global environment...
Of course it will work globally. And yes,
you decide the value individually. What is the most common outcome when an individual allows/trusts someone else (central authority) to decide the value of a currency? Why not place that responsibility in your own hands. Do you really need someone else to tell you what the value of your currency is so you can plan how to spend it? If so then stick with a fiat currency and all is well.
If trader A knows he can buy screws/nuts to create his widgets using bitcoins and trader B wants a widget and will pay for it using bitcoins there is no reason for anyone else to be involved in completing that transaction nor does anyone else need to set a price for the widget. If a third party enters into that transaction they will most definitely want their cut for whatever efforts they claim to have contributed.