Contrary to popular belief, old-timey games also suffered from the curse of the escort mission, most notably 1990's Wing Commander, a simple game about detonating spaceships cunningly disguised as massive blocks of pixels.
At various junctures within the game, you're asked to escort large, unarmed ships across enemy territory. Simple, right? Wrong. If you leave the ship's side for even a minute trying to shoot down the enemy fighters riddling it with bullets, your escortee will just speed off without you ... right into the path of the next group of enemy fighters, who'll succeed at blowing it into atoms because you're still 20 billion light years away.
That is, of course, if your escortee doesn't decide to ram you to death while you're busy trying to keep it alive.
Along with serving as a reminder of how adorable old-timey games look, the crude nature of the graphics meant that the game couldn't reliably detect where you were in relation to literally anything around you. As such, going near the cargo ship would often register as a collision, meaning that you had to fly at a distance from the thing you were supposed to be defending, which helped the mission graduate from "stupid bullshit" to "impossible bullshit."