BIP47 is first and foremost for entities who send/receive repeated payments to/from their counterparties. Examples of such entities are exchanges, mining pools, companies paying salaries to their collaborators, merchants, etc
and trying to address these entities make a lot of sense because most occurrences of address reuse are now caused by these entities. And sadly, it has a huge impact on the privacy of everybody. Silent Payments are not a better solution than BIP47. They don't even try to address the same target .
The point of the notif tx is that it doesn't require a synchronuous comm' between the 2 entities, it communicates the "identity" of the sender and it acts as a backup of the derived keys for the receiver. The partially public aspect of the notif tx is the price paid for that.
There is no server. Plus The notification transaction for BIP47 is an advantage, not a disadvantage. It makes you less likely to be dusted as a receiver and, as a sender, you don’t have to construct transactions with a taproot output - a script type that no one serious about on chain privacy uses. While SP are a magnet for dust attacks, have a significant scanning overhead for wallets and they require a taproot output in a tx too which is a negative.
the only difference between SP and BIP47 is that BIP47 requires for each output a lookup against n monitored addresses while SP requires these lookups + the computation of P0. This additional work is independent of the number of addresses tracked by the node, hence the claim that labels improve the scalability of SP
There's is still an additional load (computation of P0) but it scales with the number of outputs, not with the number of tracked addresses. Main benefit is that the former is bounded (by the max blocksize) while the latter is potentially unlimited...
Anyway Silent payments has significant performance and computational costs for the block scanning and key derivation.
It must scan every output of every block for every user. Recovering a wallet would require rescanning every output of the entire blockchain from wallets creation
Another difference is in terms of the security model associated to each mode. In the case of SP, b_scan (scan private key) must be known by the node monitoring the blockchain while BIP47 only requires public information (public keys).
