I know that interior functionality is at present back burnered (even though I still look forward to the day when my fleetmates and myself can get together for a game of poker). But I had an idea.
As I recall, there's a console on the captain's desk in the ready room. This would be the perfect interface for mail, like the consoles on the space stations. I'm tallking full featured mail where we can pick up items that are sent to us. Admittedly, this would also be a great place for contacts (how many calls did Picard take in the Ready Room), but I imagine most people would not want to zone to their interior just to get / hand in a mission.
On a related note, our bank should be available on ship as well (I don't have a specific console location in mind). I kinda think of the bank as our cargo bay anyways, so some inventory interface would just be accessing our cargo manifest.
I don't think this would really affect missions, since you couldn't access this during the mission but it saves the trudge to/from spacedock for relatively trivial things. I don't think the exchange (given its social nature) or the shipyard (can't refit in deep space) should be anywhere but the stations.
I had the same idea. You also have a trek explanation why you can access your items from the bank in different locations instantly, well because they are in your ship's cargo bay and you travel to those locations in your ship.
I also have another idea, many people are asking for the option to buy bank tabs, so lets do this in a trek way. You are not "buying" bank tabs but actually "enabling" cargo bays in your ship (all your ships). In order to enable a cargo bay (let's help Cryptic make a few more bucks ) you must spend a certain amount of Atari Tokens, this last is similar as how the bank works in Champions Online.