Well, that's how you get remote code execution vulnerabilities in CS:GO [1]. If you're doing anything at all over the network you absolutely need to care about memory safety. This doesn't mean that you need to use Rust of course, but security is still an issue.
Honk
Now of course if you use a garbage collected language, then you aren't in control of memory, so it's less of an issue. But if you are using C++ for high performance applications such as gaming, then you are in control of it and need memory safety.
We care about memory safety as much as any program. Engine code doesn't need fast compile times, scripts do, but they are scripts.
Where I have worked, we have used scripting for fast iteration.
To clarify: We have fast scripts when you want to iterate, so don't need fast engine compile times.