Thanks for thinking it through. I appreciate the time and effort.
>sidechain functionaries will not earn anything once there are at least 2 functionaries [...] they are doing all this work of validating the sidechain blocks, but gain nothing [...] the entire sidechain depends on this one sidechain functionary
I think your description is accurate, and while it may intuitively sound problematic, it turns out it does not actually cause any issues.
Even in a scenario where one entity is consistently creating all the spacechain blocks, they can only do so as long as they consistently leave 0 profit on the table for others. This is actually perfectly acceptable, because that means this entity is not censoring anyone. As soon as they try to abuse their position with censorship, it's trivial for anyone to step in and outbid them.
How trivial, you may wonder? Well, there is very little difference between being a spacechain miner and a spacechain user. Both are expected to run full nodes, the only difference is that the miner has some BTC available and is willing to use it to "mine" the block reward in the spacechain. This means that the barrier for users to act as miners is low to the point where it may happen altruistically, and, interestingly, it also doubles as an appealing way for users to purchase spacecoins in a decentralized fashion.
Btw, I personally prefer not to call a "BMM chain" a sidechain, because in my eyes it's not a sidechain if the chain has its own altcoin. The spacechain design (which avoids the use of an altcoin) comes closer to being a sidechain in that regard, but even there the use of the term "sidechain" is debatable.
I hope this clarifies things.
Cheers,
Ruben