That would only work if ALL users decided to move to SCbtc and no user wanted to buy BTC under any circumstances, even with spreads in the thousands of dollars or more. If the tech were that far superior then SCbtc deserves to win out. In reality, there will most likely be debate over which system is better and not all users will convert, resulting in normal arbitration.
People would certainly buy BTC if scBTC were worth more, but only at something less than the scBTC value in order to convert it and make a profit. There would be no reason to convert back, since you couldn't do that profitably and then sell to someone who wants to buy-and-convert, and no other demand would exist.
An objectively better chain would certainly rapidly replace an objectively worse one.
What would be peculiar in this case is if it happens while mining rewards still exist, since under the proposed side chain scheme, those are permanently tied to the main chain. In that case people will mine BTC solely for the purpose of converting it. There would be minimal transactions on the main chain (just conversions), so rewards would be the sole reason to mine. They would also merge mine scBTC for the transaction fees.
Once rewards go away, mining on the main chain would stop, and mining for fees would only happen on the side chain. A few stragglers might mine themselves (at relatively low difficulty) in order to process their own conversion transactions, or possibly everyone (other than lost coins) would have already converted.
(I don't believe mining-for-fees is workable, but that's independent of side chain vs. main chain.)