The Guard have storage because they have a huge citadel, and it comes with the added weight of not being able to do outlandish things, patrol, update a logbook, and stay within Vallaki and its surrounds. The Theatre has it because they have an extensive building and basement (though one building, still far larger than the Kinship lodge) and its supposed to be used for storing the numerous effects and costumes necessary for productions, as well as coming with the weight of having to attend rehearsals, write plays, perform them, all of that. The RVT have faction storage because their building is large (again, larger than the small lodge) and they're a merchant faction, with the goal of maximising profits; this also is weighted with IC obligations unlike the Wayfarer Kinship has. Joining these factions is maybe on par with joining the Wayfarer Kinship, but that's only half of my argument above, because these three you mentioned all require far more demanding things of the player over time to maintain membership, or have stipulations on the perks offered.
It just doesn't make sense to me that the Kinship lodge has any real room for it IC, with so many people relying on the building, and there's no faction direction reason that people need to store gear there, other than it being a convenience.