This sounds like you don't have all the answers yet.
Of course I don't have all the answers yet. But I know the basic layer is technically possible to build, and that can be improved later, because a single on-chain transaction could move coins from one sidechain to another, so making improvements will be quite easy.
Otherwise, you can try to debunk the disadvantages of Proof-of-Stake we've all remarked.
I think it should be demonstrated in practice. Imagine talking about Lightning Network without having a working system. It is hard to convince anyone it could work. So, now I am trying to write some code, and build a basic layer of what I already described. Then, I could run that as a some kind of test network, where you can easily get some test coins, just by signing some mainnet coins (that could be also done as a commitment, to make it during sending some regular transaction, so nothing more than tweaking a signature will be needed, and it would cost zero additional on-chain bytes, and one tweaked signature could commit to the hash of the block, to cover the whole test chain at one shot). Another thing is that if it will ever reach some popularity, then it could be possible to add commitments inside the coinbase transaction, just by tweaking some miner's Taproot address, that would also require zero additional bytes, and would allow reaching sidechain finality every 10 minutes, without increasing mainchain size at all. Imagine Bitcoin as a huge clock that would confirm all sidechains every 10 minutes, without any additional bytes, the whole burden of commitments will be taken by each sidechain separately.
Which were?
1) Merged Mining done wrong: they should always follow the highest source of the Proof of Work, and grant coins, accordingly to that. Having 10% of Bitcoin's hashrate should allow reaching 10% of NameCoin's hashrate, there is no need to create a separate difficulty, each chain should follow the heaviest Proof of Work.
2) No coins should be created out of thin air, they should be based on Bitcoin, may be pegged in 1:1, may be signed and cloned in this way, there were many possible solutions to that.
3) "The spent fee goes to the miners in the next block fee" - burning 0.01 NMC to register a domain is pointless, it can be done safely without it, and handled in the form of fees. Also, by throwing coins out of circulation, there is a hard limit of available domains, which is not needed.
4) Names can be attached to Bitcoin signatures or addresses, and revealed later, when needed. There is no need to explicitly include hashes.
5) No "modernised arrangement with the Merkle Tree on top" was created, no commitment-like style of revealing names was added. It should be based on sorted commitments, that should be timelocked, and then revealed in a given timeframe, to get it recorded, and committed into NameCoin, which should commit into any Bitcoin transaction every sometimes (preferably once per 10 minutes, if sidechains would get some traction, and if they would be supported by miners, and not only by users, as it is possible today).
6) "it's cryptographically possible to make a risk free trade", and we have 2022, and it is still on some TODO lists, but not yet implemented. Also, NameCoin developers didn't even try to reach that goal.
7) "A longer interval than 10 minutes would be appropriate for BitDNS" - and they picked of course 10 minutes for no reason. I thought about increasing block time on some networks, into two weeks, maybe even into one halving period. There are some nice properties, when the block time is increased (for example, Proof of Work reduction is then possible, without breaking any consensus rules, that are adjusted to faster block times, so the difficulty is then forced to drop). On some networks, it can be also decreased, like P2Pool did with their 30 second blocks, this method can be also used to do some Proof of Work fragmentation and decentralize mining, or give some people a choice between staking and mining, so they can find a balance between that, for example they could go into 90% mining and 10% staking, it is a good start, and could go further later, when people will be more convinced, that it works.
8) "In that case, domain objects (domaincoins?) could represent the right to own a domain for a year" - guess what, of course it is not "one year".
9) "You might consider a certain amount of work to generate a domain, instead of a fixed total circulation" - was it considered to utilize something like "vanity address" to have a "vanity name", where people will mine a name that will be unique, will have some matching characters, and will be cryptographically secure at the same time? Do people have a choice between paying for some characters and mining other parts? Of course not. It is not possible to mine "bitcoin" as a vanity string, and pay for "eater, don't send" to own that name. No, you have to claim the whole "bitcoin eater, don't send" part, you cannot mine names, no matter that vanity addresses are better, and they even not require a blockchain! What about mining vanity names and supporting Bitcoin Proof of Work at the same time? They didn't even start thinking about that!
10) This list is longer, but I think it will be too much offtopic. Maybe this reply should be moved to some NameCoin-related topic, feel free to do that if needed, but also note that in all of those points, you can put "Proof of Stake" instead of "Proof of Work", and it will still make sense, so you can also discuss it here.
Edit:
But doesn’t the sidechain need a peg? If it mirrors Bitcoin 1:1 then the transaction reward can’t be higher than on Bitcoin, and you can’t create new coins without breaking the peg, or where will the new Bitcoin be coming from?
"But doesn't the Lightning Network need a peg? If it mirrors Bitcoin 1:1000 then the transaction reward can't be higher than on Bitcoin, and you can't create new coins without breaking the peg, or where will the new Bitcoin be coming from?"
See? If you have some questions about sidechains, you can try putting "Lightning Network" in the same place, just as a thought experiment. Many times, you will see that it is quite similar, and many times you will see it is also similar to Proof of Stake, if you do the same trick, and if you notice, that there is no mining inside LN. I still wonder, why some people accept LN, not accept sidechains, and not accept staking. Those three concepts are quite similar, if you think more about it. And of course the answer is that fees will go to other nodes, as it is in LN, so "the fee", calculated as the sum of all outputs, minus the sum of all inputs, will cover only bare, minimal, on-chain requirements, the rest will flow inside channels, and will be signed in that way or another, by LN-validators, by sidechain-validators, or by some other validators.
Another part of the answer is that there is no "the peg", but "a peg", so if some mainchain is making some changes, then each sidechain can decide, where it should be pegged, because all coins up to the point of the split are identical. Also, even if the mainchain is splitted into BCH, BSV, or anything else, the sidechain can decide to not split, and to merge coins, instead of doing replay protection. Many rules can be altered, everything is always in users' hands.