Why not make real syscalls rather than emulate them using socket-like interface? Doesn't make much sense to me. For example, if you want to filter syscalls then it becomes more difficult (need to remember which type of socket it is, need to parse the structures and so on).
The original idea for netlink sockets (where the name comes from) is to be able to do some network packet processing in userspace. E.g. to do stuff like virus-scanning on TCP connections.
The situation there is exactly the opposite of a syscall, it is rather that the kernel calls into userspace to perform a helper function.
Communication with the socket is still read()/write()/..., so there are still syscalls. The userspace program will do a read() to get the next struct+packet out of the socket.
The modern, syscall-less interface for stuff would be io_uring. There, you do not need to read(), you can just get your data written into a userspace buffer that you can mwait or poll on.