It could be a "theme" that Sqaure decided to put in. I have reason to believe that Sqaure like themes, at least in their later games (have to check the earlier ones), but I can remember that FFX had a lot of water related stuff for instance, and FFVIII had various references to feathers and flower fields (the appearance of lions might have been a minor theme too.) So maybe "7" was chosen to be a theme for FFVII...