I suggested the same thing to my clan, everyone seems to think its a great idea, I don't think it will be in the game at launch, but as long as people want it then I think Bungie will do something similar to what you said.
I also thought that the ships could be your social point for linking with clan members etc. When you were floating in space between missions in the beta it seemed like a wasted opportunity for uses for your ship, maybe when your on this 'home screen' you could access a computer terminal in you ship to link to a clan menu as you described. Then when a fireteam IS formed, you could see your teams ships fly into the screen behind yours, I think it'd be a nice way to intergrate this without breaking the game façade.
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Good points. I wouldn't mind having this in-orbit or possibly even a terminal at the Tower (like the vaults).