An optional feature. Very useful for embedded and similar, but for general-purpose stuff like the web you never need anything unsafe.
> it's pretty common in both of these languages for there to be C libraries involved somewhere in the stack.
Negative. The complete stack is open source. You can browse the source code of the standard library at https://source.dot.net/ You only gonna find unsafe/dllimport for IO parts of that library where they integrate with file systems and such. All their core components are 100% managed code.
Filesystems, networking, ... Basically anything a program needs to interact with things outside its address space requires C interop and thus unsafe code. I sure hope your web server is listening on a socket because it's not going to be much of a web server otherwise.
Then there's crypto, for which the corelib defers to the OS (CNG / openssl) because doing crypto in managed code is hard.
All modern OSes are written in C and/or C++, unsafe code is inevitable there. Some people tried to fix that a few times (hardware java machines, singularity/midori, etc.), wasn't good enough.