I could imagine a wallet type where the indexer runs only from the moment Shielded Transactions were introduced, and then updates the state of the notes downloading all blocks, like Feather on Monero. This would still be heavier than a regular SPV wallet but much shorter to sync to compared to a full node, and could solve the centralization issue.
The anonymity set is indeed potentially a problem, but it is likely from my understanding that the level of privacy could be higher than with CoinJoins and thus a potentially interesting alternative.
I have not understood the proposal completely, I admit, but I think it is definitely interesting -- I see some similarities to RGB tokens, where rules and transactions are separated. It would not replace Monero/Grin/Zcash but simply introduce a new option for Bitcoiners, and do no harm to those not wanting to participate. Chain analysis probably still would be able to assign a higher risk score to Bitcoins coming from Shielded Transactions, running indexers and detecting patterns just like they did with CoinJoins. While this of course can harm the fungibility of the Shielded bitcoins, the fungibility of other BTC would not be touched and it thus would not change the regulation landscape.
That reminds me, one problem I think the shielded pool has (and Zcash may have had) is chain analysis firms being able to label funds coming out of it as tainted, which means that people with clean histories wont want to use it, which means a smaller anonymity set.
On the other hand I think having a local indexer is better than not, in terms of centralization risk (and starting from some point and feather-syncing may be feasible, which would help there), but running auxiliary software is probably a non-starter for the average user, so I still think most will use the public option.
That said, its similar to the RGB model in some ways. More projects are doing rules outside consensus lately.