Bit coin provides a a digital exchange mechanism, a digital wallet you (not Merrill Lynch) controls and is portable. Finally it has some degree of anonymity. But Bitcoin fluctuates wildly in value, the exchanges not regulated by any agency are run by anonymous people who are not trustworthy. (even Phil Zimmerman is puzzled why, just because he invented PGP, people assume he is trustworthy.)
If you have a stock exchange it's regulated by the SEC. the exchange is not anonymous. And the SEC can force it to have good accounting principles, audits, and proper capitalization to assure continued solvency.
Pegging it to stock at fixed exchange rate means that bitcoin's volatily will match the volatility of a stock bundle which can be quite small.
But it retains 100% of it's virtues: Bit coin provides a a digital exchange mechanism, a digital wallet you (not Merrill Lynch) controls and is portable. Finally it has some degree of anonymity.
US currency used to be on a gold standard. Since it is useful for nations to be able to devalue their currency, it went off that standard. But Bitcoin itself is not the currency of any one nation and thus there is no mechanism to devalue it.
thus this is a good idea. But the question is how to get it started.
An alternative way to peg the value of Bitcoin and have a trustworty exchange is if a country with good assets were to adopt this as the national currency or peg it's own currency to Bitcoin.
The stock bundle needs to chosen such that the companies are growing in total capitalization such that on average it approximately matches growth rate of total Bitcoin-- which is precisely known. Any difference in the growth rates needs to be small enough that arbitrager will stabilize the difference.
In short it's a great idea in principle.