Is the full-file hash actually faster than re-copying the whole file?

Re-calculating a full-file hash will require reading the whole file anyway. Which will take around the same amount of time as re-copying the whole file, since the sequential write speeds of most HDDs and non-entry-level SSDs are similar to their sequential read speeds. The only benefit would seem to be that your SSD might last a bit longer... but how many consumers use SSDs to store their backups?

Please let me know if I'm missing something.