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?