Who would you say is the Red of female player characters? No, not direct counterpart, but in status and default (This is the basis in which all female protags come from).

Kris? Her inclusion felt gimmicky for Crystal, plus she's practically forgotten by Gamefreak.

Leaf? Just his direct female counterpart. Has been forgotten by Gamefreak as well.

Lyra? LoL

Chicken? Too recent.

May? She's the first proper female protag, and has had a presence beyond Gen 3. However, she hasn't been fully canonized like Red.

Hilda? Could've become a secret boss potentially, but she hasn't really been pushed beyond Gen 5.

Serena? Well her anime counterpart is paired with Ash's counterpart, plus she looks similar to Leaf, sort of a way of updating Leaf, but she as well feels too isolated in her gen like Hilda.

Dawn? She's super popular, and has had a presence beyond Gen 4, but she isn't the first like Red is.