I understand that the difference between fold{Left/Right} and fold is that it is required the operator fed to fold forms a monoid (or in the case of reduce, a semigroup). This is mostly useful for parallel collections where a fold/reduce can be operated in parallel. However, in {fold/reduce}{Left/Right}, it is guaranteed that the operation will be done in a sequential, non-parallel way.
If so, scan doesn’t make sense. scan yields a new sequence that is inherently dependent on the original order of the sequence. Scanning in parallel does not make any sense.