And to think they never have to worry about VACUUM. Ahh the peace.
Short version is that VACUUM is needed to clean up dead tuples and reclaim disk space. For most cases with smaller amounts of data, auto-vacuum works totally fine. But I've had issues with tables with 100m+ rows that are frequently updated where auto-vacuum falls behind and stops working completely. These necessitated a full data dump + restore (because we didn't want to double our storage capacity to do a full vacuum). We fixed this by sharding the table and tweaking auto-vacuum to run more frequently, but this isn't stuff you have to worry about in MySQL.
Honestly if you're a small shop without database/postgres experts and MySQL performance is adequate for you, I wouldn't switch. Newer versions of MySQL have fixed the egregious issues, like silent data truncation on INSERT by default, and it's easier to maintain, in my experience.