It's the narrowest abstraction fitting those use cases. A database by its nature is a generic component. So sure, the piece of your software that's "SQL database" has a SQL interface, pretty quickly you'd want some abstractions on top of that around the different uses of that database.

The problem is when genericity diffuses its way into a large system it becomes impossible to maintain. How do you refactor a code base when everything everywhere is just SQL queries. If you want to change the schema how do you know you're not breaking anything? The short answer is you don't and so the software becomes incredibly brittle. The common workaround is testing but you can never test everything and now your tests also become coupled to everything else making things even more difficult to change.

The database in your example, while being generic is already an abstraction of sorts. Now if you're building lessay gmail the external users should see "create email", "get all emails", vs. issuing SQL queries to the database. That makes it easier to change the two pieces (client and server in this simplified example).