I think the KIA can fit naturally into Reti, anti-Reti play.
My objection to 1. Nf3 d5 2. g3 c5 3. Bg2 Nc6 is 4. d4! with Gruenfeld Indian Attack (GIA).
From the Black perspective, I'm considering:
1. Nf3 Nf6 2. g3 d5 3. Bg2 e6 4. O-O Be7 Black has waited long enough that White must commit to some pawn advance.
There is 5d3, leading to the KIA topic of this thread. At least both sides can hope for some play.
5.d4 may lead to a Catalan, but many of Black's more dynamic options are no longer available. Some form of main-line beckons.
5.c4 asks for a reversed Benoni. However, this is not forced. For example,
1. Nf3 Nf6 2. g3 d5 3. Bg2 e6 4. O-O Be7
5. c4 O-O 6. b3 c5 7. cd5 ed5 8. d4 Nc6 9. Bb2 Ne4 10. Nc3 Bf6 is the Tarrasch defense.