This is open source software. Even considering stealth development of a rogue sidechain, the moment they commit the code to a sidechain, the code is out there for everyone to see.
once it's determined the SC is better, the scBTC become more valuable than BTC. the arb can't work b/c the SC chain is superior and therefore the scBTC are worth more than the BTC. those who moved first will be in a better position. once other BTC holders detect this, they will start to migrate to scBTC. but the catch is: there's a cost to do so. mining fees.
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.
once miners detect this migration they will raise their fees to extortionist levels. they have to b/c accepting a devaluing BTC is risky.
Most likely processing power would leave the main chain and fees would stay relatively sane because at some point users would refuse to pay the fees.