Registry compression implemented in Registry First Aid is not like a file de-fragmentation.
File de-fragmentation is the process of ordering file fragments one after one in a sequence on a storage drive. This does not decrease or change file size.
Registry compression is the process of removing empty data blocks from a registry file. This builds a new registry file on a storage drive with decreased file size.
As there are only few registry files in an OS, their compression is similar to writing a few new files on a storage drive - this does not affect SSD drive life time noticeably.