The US actually has a history of competing private currencies since before the civil war all paper money was privately issued bank notes. Some economists have concluded that it was such a huge impediment to economic activity due to fraud, counterfeiting and the malfeasance of unscrupulous bankers that private money cost the US economy some 10-20% of GDP each year. The relative value of privately issued currency will be determined by public perceptions of its value relative to other issues and the activities of speculators on the money exhanges. Your Wal Mart dollars may only be worth 80 cents at Starbucks this morning but worth $1.10 on the afternoon. You get paid in Target dollars but you have to pay your mortgage in Goldman Sachs dollars. The exchange rate has risen to 5 to 1 overnight, more than your entire monthly income. Imagine this multiplied a thousand fold. The economic friction of highly variable exchange values is a huge problem already in international trade. To multiply that in the US by allowing private currency issues is a truly insane idea.
Actually, we don't have to imagine competing currencies. Every European country used to have their own currency. I don't remember the exchange rate between different currencies, like the Drachma and the Deutschmark, every changing by fivefold over night. The Drachma/Deutschmark Exchange Rate, 1980 - 1997: A Monetary Analysis Professor Papadopoulos did not find any such variability either. But if you insist that having competing currencies is "insane," then perhaps you could supply us with a quotation from a modern Greek economist extolling the stability of the common European currency? Note: You might have trouble finding a modern Greek economist who hasn't lost his job in the recent budget cuts. So, if you need a quotation extolling the stability of their current system, you had better hurry before they all hit the exits.
There is a large difference between the motivations and controls on national currencies and private currencies so your consideration of their positions in economies as somehow equivalent is irrelevant. These national currencies did not compete in their respective domestic markets. You could not easily spend Greek Drachmas in Germany. Even so, national currencies have often experienced huge inflation and exploding exchange rates over very short periods. Germany in the 1920s and Argentina in the 1980s are some examples that come to mind. If you really want to learn how private currencies functioned in the real world you can read "A Nation of Counterfeiters" which is a short history of privately issued currency in the US. The streets around the currency exchange in New York were perpetually littered with private bank notes that the exchange had deemed worthless.
Is that the only book you've read? Very well. I will read - or at least skim - it, but only if you read my 2006 paper, Critique of Stephen Zarlenga on the Origin of Money. However, if you wish to debate the merits of having different currencies in different regions or countries, such as Europe once had, compared to a single currency such as the Euro, then start a new thread. Such a discussion is off-topic on this thread because Ron Paul's proposed legislation, HR 2768, finds theoretical support in the Debt-Virus Theory and NOT in Austrian Economics. Give the man an "A" for clarity! Whatever else you may think of Zarlenga, at least he is not a liar. Unlike Ron Paul, Zarlenga is not trying to pull the wool over our eyes with some ****-and-bull story about multiple currencies of the type that Europe once had. This is basically what HR 2768 would do: subsidize state-run industries and agriculture with uncovered monetary emissions.
In the U.S. that would be the Department of Education. I don't know what the English call their collective provision of education into socialism.