I think the first round of a dropship insertion should have smoke all around, fired by the dropship to give the soldiers a chance to reach cover. By the second round, I think the dropship should be leaving, to prevent aliens from entering it and capturing flight crew and navigational data. In game a small cutscene video in the corner could do for the dropship taking off, and then when the next round starts, it's just not on the map any more.
If you think about it, the aliens watched the ship come in, and watched the humans get out of it. It doesn't make much sense that we get the first shot on them.
It would be kind of cool to be able to use a supposedly orbiting dropship for support fire from off the map, depending on the loadout of the ship.