Why would you call this a "mathematical" flaw? Your original post implied there was some algorithmic issue, when you're really just proposing dumping the exchange market -- which is a completely independent mechanism of trade.

> Also the only way to get bitcoins securely is to buy and sell them for cash. And even then there are ways of figuring out who is who.

This is ridiculous. The psuedoanonymity of bitcoin allows for laundering services which enhance your plausible deniability. You can't practically figure out "who is who" if I send a delayed transaction through a popular laundry service.