I think those of us who saw Luna's implosion know what would happen if such a thing was repeated here.
For example, if a smart contract were to issue 1 sideBTC in exchange for 1.001 BTC, and were to redeem 1 sideBTC in exchange for 0.009 BTC, the value of 1 sideBTC would always remain at approximately 1 BTC, and market transactions would most often make it so redemptions/issuances would be unnecessary.
The problem here is that you shouldn't need an algorithm to regulate the price of the sidechain BTC.
See, 1 LN-BTC = 1 BTC not because Lightning Network is regulating the price but because it bulletproofed the network implementation from hacks and flaws - the only way you'd be able to change the price of LN-BTC anyway (which is down to zero) - you don't need an algorithm when you have two layers of a coin that ultimately use the same network*.
*I did not say "tokens" because these have algorithms that actively try to make the price different from the main coin.**
**Coinbase has a wrong definition for "token" here: https://www.coinbase.com/learn/crypto-basics/what-is-a-token (the first one) which everyone should disregard to avoid muddying the waters further.