I fully recognize that political definitions drive purchases, so it's meaningful to a project either way. but that doesn't make it a valid technical argument.
If it can avoid crashing, other functionality may continue to work fine.
But the choice is not just political. There are very meaningful technical differences for code that potentially winds up embedded in other software, and could be inside of literal embedded software.
The first is memory. It takes memory to run whatever is responsible for detecting the crash, relaunching, and starting up a supervisor. This memory is not free. Which is one of the reasons why Erlang requires at a minimum 10 MB or so of memory. By contrast the overhead of SQLite is something like half a MB. This difference is very significant for people putting software into medical devices, automotive controllers, and so on. All of which are places where SQLite is found, but Erlang isn't.
The second is concurrency. Erlang's concurrency model leaks - you can't embed it in software without having to find a way to fit Erlang concurrency in. This isn't a problem if Erlang already is in your software stack. But that's an architectural constraint that would be a problem in many of the contexts that SQLite is actually used in.
Remember, SQLite is not optimized for your use case. It is optimized for embedded software that needs to try to keep running when things go wrong. It just happens to be so good that it is useful for you.
This state can be "the database is corrupt", allowing for a restore from backup, it can also be "shut down gracefully" and communicate that.
Especially for databases there is a ton to concinder: what about database entries that are not committed yet? When you run into oom, should you at least try to commit the data still in ram by freeing as much space as possible?
The use case that SQLite has chosen to optimize for is critical embedded software. As described in https://www.sqlite.org/qmplan.html, the standard that they base their efforts on is a certification for use in aircraft. If mission critical software on a plane is allowed to crash, this can render the controls inoperable. Which is likely to lead to a very literal crash some time later.
The result is software that has been optimized to do the right thing if at all possible, and to degrade gracefully if that is not possible.
Note that the open source version of SQLite is not certified for use in aviation. But there are versions out there that have been certified. (The difference is a ton of extra documentation.) And in fact SQLite is in use by Airbus. Though the details of what exactly for are not, as far as I know, public.
If this documented behavior is not what you want for your use case, then you should consider using another database. Though, honestly, no other database comes remotely close when it comes to software quality. And therefore I doubt that "degrade as documented rather than crash" is a good reason to avoid SQLite. (There are lots of other potential reasons for choosing another database.)