However, by that measure bitcoin has already achieved success. The bitcoin network currently mediates between 50 and 60 thousand transactions every day, transferring an estimated 70 million USD every day.
As far as bootstrapped nascent currency experiments go, bitcoin should certainly fulfill many criteria for "success" already.
Curioulsy the number of transactions per day and their total BTC volume have increased very little, or not at all, since September last year. So, either commercial e-payments are a small fraction of those numbers, or they are not increasing (and their USD volume is actually decreasing, since the BTC price has fallen considerably in that period).
Actually, the number is almost twice as high. (use "exclude popular addresses" because: dust from gambling sites)

Does the increase in transactions perfectly motivate price increase? Maybe not. Or at least, it's an open question (see gbianchi's model, for example)
Does the no. of transactions rise very obviously in an exponential fashion? You'd have to be pretty biased to deny that.
And there it is, one of the "fundamental reasons" for price growth you keep looking for.