Because many customers have their own expertise in the database system of their own choice. A shop that has hired Oracle DBA's doesn't want to hire Postgres folks. A MySQL based place doesn't want to hire Oracle folks. And they already have built extensive data-management processes around their choice of database systems and have the in-house experience to manage their database system in a wide variety of platforms.
If you to sell a packaged, deployable product to the widest market, yet want to minimise support, you leverage the expertise that the customer already possesses.
This is probably more of a consideration in the business enterprise space than some simple normal end-consumer SaaS, so I am not saying this approach makes sense everywhere.
I've seen this type of thing before, but it's not a common use case (and I'm not sure why people still do it).
It makes more sense to just say that the product uses a FOSS RDBMS (like Postgres) and leave it at that. There's no vendor lock-in.