The Fleet/Rep system (just like leveling/experience points) could remain per character, as long as the needed currencies (Dilithium, Marks, etc.) were freely unlocked, and the resulting gear was account (instead of character) bound.
These freedoms could be restricted to characters-per-faction. So all Feds on the same account shared currency. All KDF had a different currency pool. Future Romulans, etc. This would require the player to play the missions for each faction, but otherwise still allow some sharing.
Perhaps restrict this to just Gold Members, thereby increasing the value of paying a monthly subscription (which currently there is very little reason to do so).
I can also understand them putting an account-limit on daily dilithium earnings.