Therefore, the peg with no restrictions in conversion volume will necessary make value either move fully to bitcoin, or fully to the sidechain.
That doesn't make much sense. Can you explain your thoughts on the mechanics of that?
That makes all the sense there is. It is the basic function of a market. If you try to fix prices, you will either have to much or too little goods. For instance in a business, if you fix wages below the market, the business will have problems finding workers. if you fix the wages at a higher rate than the market, there will be a queue of workers outside. If there is no quota in the gates (two way pegged sidechain), all workers will be hired in that business.