Yes, actually it does. If, for instance a large volume of trading were done with goods of any manner that had a fairly stable value denominated in the US Dollar then Bitcoin would become correlated with the Dollar, and this would make the exchange rate with the Dollar more stable. This is what everyone has been saying, including you, but in different terms.
Last time before I drop it: A large volume of goods trading integrates Bitcoin into a larger economy. This causes: 1) correlations; 2) stability. It does not cause correlations which in turn cause stability. The correlations are just the consequence of being part of a larger economy.
But this does not solve the problem of market depth on its own. A low price would demand a relatively large exchange trade volume to prevent a liquidity crisis in the event of a large buy/sell. As long as the exchange rate remains at a low level the utility of Bitcoin remains limited to small purchases. As soon as a largish exchange has to be made to execute a purchase of some sort then the price will swing all over the place. The likelihood of this happening with a high exchange rate is lower than with a low exchange rate. Apples to apples, a high exchange rate will have less volatility than a low exchange rate.
I agree with everything you say here. I disagree that propping the price up helps liquidity. Unless it's backed by large amounts of commerce (and therefore trade volume), it's just a high price in a thin market, and therefore subject to high volatility... Even worse than a low price, since a propped up price drops whenever the fleeting interests of the price-proppers changes.
The high price is an effect, not a cause. You have to create the root cause: commerce, which creates volume, which creates depth, which creates stability. Note that "price" isn't in that chain: it's a sibling of volume, an effect of commerce; artificially recreating a correlated sibling effect (high price) does not magically recreate their common cause.
It's like saying that land with lots of wildflowers makes a good place to grow crops. Sure, they correlate - because they have good soil, rain, and sunlight. But planting flowers everywhere doesn't make the land good for farming.