Instrinsics more or less map to specific assembly instructions, but the instruction scheduling and register allocation is still handled by the compiler, which you have to do by hand in raw assembly. Possibly multiple times, since the optimal instruction scheduling is hardware specific. Intrinsics can also be automatically inlined, constant folded, etc, which you don't get with assembly.

Also Intel and ARM themselves specify the C intrinsics for their architectures so they're the same across MSVC, GCC and Clang, it's not like the wild west of other compiler extensions.