I'm sure I won't earn any favors by letting you know this, but it does seem to go against the design and can cause bugs;
If you have completed an assignment and are on cooldown, you can currently still accompany others who are doing assignments by joining them as they leave for the mission (after the new assignment has been given to the different player), this can then be used to "cycle" assignments per player or group/half group, essentially making it possible to repeat these quests almost nonstop (granted you won't get the xp reward every time, but you get all the loot and kill xp).
I understand why the cooldown is there in the firstplace (for limiting the xp farm potential), but you could make other workarounds for this, for example the traveling speed on the world map is very fast, you could slow it down exponentially and make the assignment locations a much further distance away from base, the forced travel time acts as a physical time barrier removing the need for a cooldown timer. If the random encounters were functioning too, this could make the time taken to travel to and fro extended by the element of randomness. It also makes the idea of redoing the quests more of a functional challenge than an annoying timer.