To be fair, obtaining reputation with a faction and the faction's actual purpose in the tower are two different things. Like, if you take down a Gate Lord (for a bounty) in the name of Dead Orbit, fair's fair, I'm sure you'd gain reputation with Dead Orbit for doing that, but it explicitly states that Dead Orbit only maintains a presence in the tower to outfit guardians for the Crucible, hence the Crucible marks. I can't speak for New Monarchy or Future War Cult, but it makes sense for Dead Orbit at least.