Nobody has just one app forever. Any org that gets big enough is going to be uncertain about how many apps depend on a particular database, much less whether they’re all in the same language and bundle the same schema rules. Customer service builds weird support tools, accounting and compliance build weird reports …
In reality sometimes access via an API is way too slow or is lacking flexibility.
And I don't get this: "(e.g. if you have multiple applications writing to your database in transactions then you're virtually guaranteed to get deadlocks)"
Isn't this why transactions exist in the first place?
While MVCC avoids deadlocks, you'll still get a lot of failed transactions if they all operate on the same data at the same time, which you'll have to retry, but I'll take that over data inconsistency
That assumption is only true if the DB is continually used by different applications. The reality is more likely a large number of applications used by a relatively small set of users, so most of the time there won't be any application writing, and it would be extremely rare for multiple applications to write at the same time.
(But indeed, with uncoordinated development, deadlocks can occur. Still better than data corruption.)