MySQL replicas self-recover via MASTER_CONNECT_RETRY and MASTER_RETRY_COUNT. e.g. set to 1, 8640000 respectively to make a replica retry every one second for up to 100 days before finally giving up.
At least this is true for network errors. If replication breaks due to data inconsistency, it should stay broken and a human should look into it, IMHO.
Corrupted tables and repairs suspiciously sound like MyISAM, and a realize this ancient engine still lurks at some places. I haven't done a "repair" for over 14 years -- the last time I used MyISAM in production. Using MyISAM today is analogous to using the ext2 file system today.
In any case this just clarifies a couple comments on MySQL and has nothing to say on MySQL vs. PostgreSQL.