Sure, but the borrow checker only operates on references. Rust gives you the tools to work with raw everything, if you dip into unsafe. Memory allocators, doing this kind of low-level thing, don't work with references. Let's say you want to implement a global allocator (this is the only current API in stable Rust, non-global allocators are on the way). The trait you use, which gives you the equivalent of malloc/free, has this signature:

  unsafe impl GlobalAlloc {
      pub unsafe fn alloc(&self, layout: Layout) -> *mut u8;
      pub unsafe fn dealloc(&self, ptr: *mut u8, layout: Layout);
  }

Note the *mut u8 rather than say, &mut u8. Most people would not be using this interface directly, they'd be using a data structure that uses it internally.

Now, there's a good argument to be had about safe and unsafe, how much you need, in what proportion, and in what kinds of programs... but when you say things like "C allows you to do bulk memory operations, Rust does not" and ask about the borrow checker when talking about allocators, to someone who is familiar with Rust's details, it seems like you are misinformed somehow, which makes it really hard to engage constructively with what you're saying.