I don't think the government minds alternative currencies. The possibility of easily shifting large amounts of currency anonymously, I think, is what the government has a problem with. Because green dot checks id, etc... it's not a problem. If E-gold asked for your ID, your SSN and reported things as a bank would from the beginning, I don't think e-gold would have had an insurmountable problem, either.
By "private" I meant "allows anonymous users" not "owned by someone other than the government." which is very unclear. I've been up all night working and my grammar is degraded.
If someone could buy a prepaid debit card for cash without showing ID, and add money to it without showing ID, and spend from it without showing ID, then Alice could buy a card, Bob could load $5000 onto it, and Carol could read the card number over the phone to David. To achieve the same kind of anonymity today, someone would have to accumulate $5000 in cash and put it in David’s physical possession.