This scheme works for FITS (the Flexible Image Transport System, see ref. 1-5) data as for other data, but separating the checksum from the FITS file limits its utility, especially for archival storage. It is also hard to see just how to incorporate a separate checksum into the FITS standard.
The internet checksum (ref. 12-14) resolves the similar problem of embedding a checksum within each IP packet by forcing the checksum of each binary packet to the same value (zero). This works by writing the complement of the calculated checksum into the packet instead of the checksum itself.
Arranging to write a binary number into a FITS file is unattractive and limiting. However, the properties of commutativity and associativity that make the internet checksum work in the first place, also make it possible to generalize the technique with an ASCII encoding that may be embedded within a FITS header keyword (ref. 8).