Singly and doubly linked lists have the identical (terrible) linear access time. Using doubly linked lists would not help performance. The only benefit you’d get is that reading file backwards is more efficient.
No modern file system uses linked allocation anymore. Most use ranges of consecutive blocks, so called extents. Extents are usually more space-efficient and support random access. Neither Singly or doubly linked lists support random access. In practice these days the metadata for a file is read in at once (with all its extents), this is fast. Reading all nodes of the linked lists would mean reading several blocks, one after the other. This is slow, obviously.