What are good reasons to update proof-of-work algorithm from the current SHA-256d?
None, I guess. If SHA-256 is not broken, then it should be used as it is. However, a lot of altcoins changed the way their coins are mined, just because they didn't know, how to do it properly, so they did, what they could.
Also note, that you don't even have to leave SHA-256 world, to make some ASICs obsolete, if that is your main goal. A good example of that is Proof of Work inside Script, where the same SHA-256 algorithm is used, but many ASICs won't help you produce a smaller DER signature, because the whole format is different:
https://bitcointalk.org/index.php?topic=5551080.0solving the problem of centralization. Do you agree?
No, because if big mining pools can already use SHA-256, to produce a stronger chain, then if you assume, that your coin will be successful, then they can switch to a new algorithm faster, than regular users, when it will be profitable enough. Who can upgrade faster, when needed? Some owner of a warehouse of ASICs, and a bunch of EH/s, with years of expertise in the field? Or a random user, who only did some home mining, with a few TH/s at best?
Do you see more pros and cons?
There are more cons, because BIP-110 chain already mined four blocks, at the time of writing. Which means, that it has enough power, to produce new blocks, every sometimes, with the biggest SHA-256 difficulty in the world. Changing Proof of Work means, that all of these EH/s will be gone, and instead of being used to push BIP-110 forward, they will be splitted into mining other coins, because ASIC owners will want to recover some of their costs, so they will keep mining other coins, just to sell them for dollars, and then maybe buy some BIP-110 coins for that.
You have one piece of work. If you solve it, it will solve a block from both Bitcoin and BitDNS. In concept, they're tied together by a Merkle Tree. To hand it in to Bitcoin, you break off the BitDNS branch, and to hand it in to BitDNS, you break off the Bitcoin branch.
Satoshi already described, how to use Merged Mining, to work on more than one chain, with the same hashing power. In general, if you have a split, and you want to have different chains, for different use cases, then this is what you want to use.
However, because BIP-110 is a soft-fork, and it is designed to not use Merged Mining, it is a bit different story. If you really believe in soft-forks, then you would explore further the idea of weak blocks: this is how P2Pool was successful, and produced blocks every 30 seconds, which were 20 times easier to make, and their subnetwork was compatible with the main network. Here, the BIP-110 chain is not immediately open for all kinds of attacks: as long as you can implement fractional confirmations, and weak blocks properly, you can unstuck the chain, without any hard-forks.
But well, people didn't listen back then, when they were told, that the speed of the chain will be proportional to the signalling vs non-signalling hashrate. They ignored all technical feedback, without testing things, and checking, what is a valid criticism, and what is not. There was not even a testnet for BIP-110, which could tell its proponents, how things may turn out. So, I also expect this time, people will also ignore soft-fork ways of solving the problem, and some kind of hard-fork, with a new hashing algorithm, will be deployed. But then, all old posts, claiming that BIP-110 is a soft-fork, can be quoted, and commented as "if this part was a lie, then how can we believe in your present words?".
Another thing is that if the mining algorithm will be changed, then all existing BIP-110 nodes will be obsolete. Then, what will be "the true BIP-110?". After doing a hard-fork, absolutely everything can be deployed. And at that point, it will be not much different, than launching a new altcoin. And of course, all mathematical chances to ever reorg non-BIP-110 chain will be destroyed, because of making backward-incompatible changes.
Edit:
What are good reasons to update proof-of-work algorithm from the current SHA-256d?
If the Proof of Work algorithm will be broken, then it should be updated.
SHA-256 is very strong. It's not like the incremental step from MD5 to SHA1. It can last several decades unless there's some massive breakthrough attack.
If SHA-256 became completely broken, I think we could come to some agreement about what the honest block chain was before the trouble started, lock that in and continue from there with a new hash function.
If the hash breakdown came gradually, we could transition to a new hash in an orderly way. The software would be programmed to start using a new hash after a certain block number. Everyone would have to upgrade by that time. The software could save the new hash of all the old blocks to make sure a different block with the same old hash can't be used.
However, it is not the case, when it comes to BIP-110. Also note, that if SHA-256 will ever be broken, then it can be fixed in a soft-fork way, by requiring both SHA-256, and some new algorithm, for exactly the same block data. Because breaking hash function will lead to more blocks being produced, than usual, so a new hash function will be needed to slow it down, and secure the chain again.
If anything, you probably want to unstuck the chain, so the simplest hard-fork you can make, is to allow blocks with any difficulty, after 20 minutes, just like testnets did. It is the fastest change, that you can deploy, because it is already coded, and it is all about enforcing it after a given block number. Or, you can always use weak blocks, but it requires more coding, but again: P2Pool is Open Source, and you can adjust the difficulty, based on time, where no blocks are seen. Then, the subnetwork with 10 minutes per weak block can unstuck users, and every sometimes it can turn into a valid on-chain block, with a valid difficulty.
