M201 Ch2 Compound Index: why not use index for out-of-order key pattern query?

For a collection that has a compound index on {first_name: 1, last_name: 1},
we can make use of index for queries including prefix

  • find({first_name: ..., last_name: ...})
  • find({first_name: ...})

But why not use index for a query like find({last_name: ...})?
MDB runs COLLSCAN wherein all documents must be read into memory.
It’s like

  • nReturned: n
  • nIndexExamined: 0
  • nDocExamined: N

However, index is already in memory. So if it runs IXSCAN, it will be like

  • nReturned: n
  • nIndexExamined: N
  • nDocExamined: n
    If n << N, the benefit becomes huge.

Is it because the index has no demarcation among keys in it?