The same value can not be held simultaneously in the main chain and in a side chain.
But the value of the sidechain is derived from the mainchain and so the scarcity and ledger is respected.
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.
That is correct, but this value only exist because it was derived off the Bitcoin mainchain.
I think the concern is : does this value sitting on other chains respect Bitcoin's ledger and the answer is in the most probable cases it does.
Convertibility then is the feature by which all of this value sitting on different chains is compounded. Of course if the peg is removed than the value on any of the detached sidechain is cutoff from the ecosystem.
Is that a problem? It is, but not one that sidechain introduce. There exist plenty of off-chain schemes already that are in fact more probable to corrupt the value assigned to them, IMO. Sidechains that are properly implemented will protect the value assigned outside the mainchain on the procol level.