During the dot com era it was common to develop and launch on MySQL with the intention of migrating to something else if they became successful (though your typical LAMP stack developer regarded Oracle and SQL Server as being deeply 'weird', so many were willing to stick with MySQL despite the well-known limitations of MyISAM).
From where I'm standing, it seems that PostgreSQL became clearly preferable for new projects from the mid 2000s onwards, but it was only the Oracle acquisition that began to push existing users off MySQL.
edit to add: MySQL did have operational advantages even later than mid 2000s since it had master/master replication from very early (I don't know how sound it was, I doubt it was perfect). That was a real reason to choose it. We still don't have it in Postgres without extensions and even there citus is not really the same.
(I remember it being heavily touted in the first edition of the O'Reilly "High Performance MySQL" book. The second edition was about twice the length, with most of the additional pagecount going into detailed explanations of why you should actually be very careful and do lots of testing before deciding to rely on master/master!)
Actually, I remember that one of the drivers away from MySQL before Oracle came along was the 4.x and 5.x period, when there were various performance regressions. And even when those were sorted out, the introduction of InnoDB made people realise that MySQL's apparent speed advantage was really just down to MyISAM lacking referential integrity and transactions.
Certainly, there were people clinging on to MySQL 3.23 for read-heavy data warehousing applications for a very long time.
Yes we saw the same thing play out with MongoDB. Ack without fsync is indeed very fast.