It's the same reason why you don't get attached to people you just occasionally see shopping at your local store as opposed to getting attached to your friends, relatives, classmates, coworkers...
For the players, Tifa, Aerith, Barrett, etc. are acquaintances at worst, friends at best. Jessie, Biggs, Wedge are generally just "people you've seen a few times" for most players. Also, this is not meant to be dismissive, it's just explaining why the general trend is getting attached to the popular characters.
Anyway
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