I don’t think either DB is bad, but the whole MySQL is dead and needs serious work idea doesn’t make sense to me. What problem does MySQL still have that needs fixing in your opinion?
Anyone who says no investment has been into MySQL I suspect never took the time to read the features/release notes for MySQL 8
Very recently they've mentioned they'll be changing this again to have separate LTS releases, which is a positive change stability-wise.
Facebook definitely has the resources to migrate to Postgres, if there was any motivating reason to do so. Indeed, Facebook developed their own LSM-based key-value store (RocksDB) and MySQL storage engine based on it (MyRocks) and then migrated the majority of their db fleet to that. In total that's massively more work than migrating to Postgres would have been.
Part of the reason was that MyRocks provides better compression than pretty much any other possible choice, and that adds up to an astronomical amount of cost savings at Facebook's scale. In contrast, what would Facebook have gained from moving to Postgres instead?
I'm unfamiliar with Faire but the rest were already using MySQL at the time of Oracle's acquisition in 2010. Switching backends would have been rough for those companies and this was... 2010, meaning Postgres was not nearly as performant or full featured as it is today. As mentioned in other comments, FB's investment in customizing MySQL has been extensive. They've poured a lot into their own fork of it.
More to the point, look at MySQL's progress since 2010. Do you think it has been largely stifled since then, or do you think it has kept pace with Postgres? It's been largely stagnant.
I'd love to hear your alternative theory, of course. You think Oracle bought MySQL to... what, exactly? Make it amazing?