postgresql 13 sync replication implementation question and pgpool failback question

In a pgpool-II 4.2 and postgresql 13 environment: 3 servers (each hosting a pgpool and a postgresql)

I understand we can set the below parameter for different durability’s. synchronous_commit = off, local, on, remote_write, or remote_apply

My question is that when I set it to something beyond "local" document implies the wal information will not even be sent to slaves until the local is flushed.

My question is why not the below 2 start in parallel

  1. local flush starts
  2. sending wal info. to slaves

because this would save some time by doing these in parallel, correct? Or please let me know my understanding is off?

The other question is that does pgpool-II simplify the postgresql failover and failback? And is it reliable? Is there some real life examples of setups and comments on this? Thanks!