As far as HA goes, that abstraction can then go toward allowing your apps and DB to be built for different reliability/durability/etc requirements, potentially saving money, gaining better performance or reliability, meeting weird compliance requirements, contractual requirements, vendor or software limitations, etc.

It's also easier to troubleshoot and maintain the database separate from the application in some circumstances. If SQLite is bundled with your application, it might be harder to deal with a problem affecting one or the other. In traditional organizations, you can hire people to manage databases and people to manage applications, rather than one person who has to deal with both, or even weirder, two people that would be working on one db-in-your-app.