At least it has an optimization that if the insert ends up in the same page, it won't need to update the index https://www.postgresql.org/docs/current/storage-hot.html
Replication has a similar amplification issue. Historically postgres has favored physical replication over per-row logical replication, that means that replication needs to transfer every modified page, including modified indexes, instead of just the new value of the modified row. (I think logical replication support has improved over the last couple of years).
There is the OrioleDB project, which attempts to improve on the design flaws in postgres's storage engine, but it's definitely not production ready yet.