do you seriously think that when a SC is first established on Day 1, 1 scBTC = 1 BTC in fiat terms?. it can't be b/c of newness, less security, chance of failure, etc. with time, as it proves itself, the arb bots will equilibrate the price but at a lower level b/c of the always present risk of failure of the SC. the SC is not Bitcoin.
Before the arb bots can work, first there has to be people who hold sidechain units who are willing to sell them for fiat at a loss instead of converting them back to Bitcoin.
I'm not sure what the mechanism for this would be.