Except with a two-way peg, each of the sub-operators are completely dependant on the backing-store as their value basis. If it fails, they fail. Think of it as having a monopoly on the wrenches needed to keep any bus healthy no matter who owns or runs the buses. They have no choice but to keep the backing store solution healthy.
As I say, there is clearly a lot of value to be had by a merchant in getting consumers on-board as evidenced by the the rewards programs. A small fraction of this passed on to a tight and secure backing store (hopefully native Bitcoin in it's current 'free' form) may well be many many times the value to be had by simplistic transaction fees or even by the current rather high inflation rate.
You see, this is where I think the reality disconnect starts with sidechains. Are you suggesting that there is going to be a 1:1 peg by value with the token ( and I use that term generously, altcoin could also fit) used in the transport channel/sidechain and the value of the transaction being represented? E.g. If I want to transfer $100 fiat from my US office to my European branch via a company operating a sidechain, that the Bitcoin equivilent of $100 has to be 'locked' on the blockchain?
So in essence, the availability of the transaction is directly tied to liquidity in Bitcoin? So if a sidechain operator wants to offer to transfer $100m, they must find and secure the equivalent Bitcoin. Sounds tricky.
What if it could be a 1:100 or 1:100,000,000 peg, as per my bus stop analogy?
You need to be able to visualize ratios.
When I say 'one-to-one', I'm not even indicating that individual sidechains would not have their own inflation/deflation. I fully expect that many of them would. People who decide to own coins on one sidechain or another would need to factor the management of a sidechain into their decision.
Sidechains when viewed from above would be rated specifically on how many Bitcoin's are pegged.
1) foocoin has 1000 BTC pegged to it. It's a '1000 BTC sidecoin.'
2) There are 10,000 foocoins. Thus, there are 10 foocoin to the BTC.
3) Tomorrow the foocoin project changes to a circulation of 20,000 foocoins.
After #3
foocoin remains a '1000 BTC sidechain' irrespective of the internal circulation decisions.
As a user one needs to have confidence in the management of foocoin. If you cannot achieve that confidence, don't buy any foocoins. If you start to lose confidence, excersize your peg and bail back into Bitcoin, or move directly to another sidecoin.
What developers like Blockstream can do is to provide the tools so that you can protect your stake in the backing store. For instance, mathematically gaurentee that if the foocoin circulation changes by more than x% in x amount of time, you automatically revert to holding the backing currency (which would be Bitcoin unless Heardresen destroy it as a 'free' currency first.)