But the value of the sidechain is derived from the mainchain and so the scarcity and ledger is respected.
This is a very interesting theoretical question: "where is the value stored for a sidechain?"
Let's do a little thought experiment to try to come up with a reasonable answer. The purpose of the thought experiment is to isolate the effect of the 2-way peg; it's meant to be a tool to help us understand where the value is actually stored, and not meant to represent plausible future scenarios. We'll ask what happens to the value of scBTC should the 2-way peg be instantly and permanently severed (and the locked BTC on the main chain frozen). If one argues that the value is always stored on Bitcoin's Blockchain, then I think in all cases the value of scBTC should fall to zero. It's pretty clear to me that that won't actually happen in all cases:
Case #1: Small sidechain backed by 0.01% of the main-chain BTC
Here we have a small sidechain used, perhaps, for experimentation with faster confirmation times. Very little real economic activity takes place on this side chain. When the 2-way peg is severed, I believe the value of scBTC#1 would drop rapidly to zero, as everyone would realize that another sidechain employing the same features but maintaining the BTC backing could easily be recreated. The network effect is too small to matter.
--> value is stored on Bitcoin's Blockchain.
Case #2: Large sidechain backed by 10% of the main-chain BTC
Here we have a large sidechain that perhaps employs ring-signatures for improved anonymity. This scBTC#2 has become the token of choice for black-market activity such as the purchase of illicit goods from SilkRoad 3.0. When the 2-way peg is severed in this case, the value does not fall to zero. The value immediately drops, because many individuals would prefer to hold BTC than unbacked scBTC#2. However, it does not drop to zero because speculators and scBTC#2 users realize that the huge network of users and wallet infrastructure already set up to accept scBTC#2 will maintain demand for unbacked scBTC#2. scBTC#2 becomes an alt coin and trades with a floating exchange rate with respect to main-chain BTC.
--> value is stored in both Bitcoin's Blockchain and the sidechain ledger.
Case #3: Uber sidechain backed by 60% of the main-chain BTC
Here we consider the case where the majority of bitcoins are stored on the sidechain. Perhaps this sidechain is just "better" than bitcoin, and there's a huge push by merchants to move all economic activity here. Speculators also decide to move their BTC to this sidechain, as they fear that a severing of the 2-way peg would hurt the value of their main-chain BTC (they see that the network-effects of this sidechain are becoming greater than Bitcoin's). Now when the 2-way peg is severed, I would argue that it would be the value of bitcoin that would fall and the value of scBTC would actually rise! Scarcity of scBTC#3 is actually greater once the peg is severed (no more main-chain BTC can be converted) and since the majority of economic activity is taking place on this chain, the ledger for scBTC#3 becomes the dominant "memory" for our money.
--> value is stored mostly on the sidechain ledger.
Once again, the purpose of this thought experiment was not to propose "realistic scenarios"; the purpose was to help answer the question "on which ledger is the value stored?" I think the answer is that for low-levels of adoption, the value remains stored on Bitcoin's Blockchain. But as the network effect of the sidechain grows, a larger component of the value is actually stored on the sidechain's ledger.
Value = convertibility + utility
And in all 3 examples is decided by market forces.
Failure modes are usually one of the best places to start looking for the hooks.
How does something fail? How can it be made to fail most safely, and in what ways can it not be made safe?
I would consider the effects of different failure modes on these scenarios.
They start with the assumption that the 2wp is broken and that convertibility is lost but this can happen in many different ways and for different causes.
The BTC may remain locked or not in different types. If locked and no convertibility they are burned and deflate BTC, or they may be unlocked and re-inflate BTC. Or there are hybrids.
In one of the previous examples we had:
MC
| \
| /
SC2
Where SC1 had rogue devs/miners who inflated it with new assets or subverted the proofs so no SC2 would convert back to SC1 and so convertibility was lost.
Subsequently SC3 is set up to restore convertibility because SC2 had such utility that it kept going and new owner folks wanted to (somewhat) regain the convertibility aspects (including new issuance from SPV).
So now you have SC2 with some BTC convertible back to MC and some not.