Making a character that both isn't a complete idiot, and that you actually grow attached enough to want to protect.
This is mostly going to be revolving around two examples: one that I do have familiarity with and one I don't. I'm hoping that by looking at what makes escort missions less of a burden that I can come to an understanding of how a game designer should go about making a better escort mission in the future.
For the example I know I'm going to turn back to Resident Evil 4. I know that I harped on the game yesterday, but like I said it has some of the least annoying escort sections that I've ever played despite meeting the major criteria of escorts: uncontrollable character, can't defend herself, and game over if killed or otherwise indisposed. However, there are things (both good and bad as I see them) that help mitigate a lot of the trouble.
First and foremost is that unlike some other NPCs, Ashley does not have a tendency to wander around on her own. If you instruct her to stay somewhere she will unless an enemy happens upon her and tries to carry her away at which point you'd be alerted to it anyways. When instructed to follow you she'll always go behind you the best she can and if you do end up having to shoot while she's in front of you she'll actually duck and cover so that she won't be accidentally shot or rather at least not shot as easily as if she just stood there dumbly.
Something I mentioned last time is that there are certain points when you can have Ashley get into a relatively safe location like inside a dumpster. While she's in here it's almost guaranteed that she won't be found and you can clear the area in relative piece as though she wasn't there. Although this is a much less annoying option than having her tag along and risking her getting carried off or killed it sort of feels like a cop-out. Why even bother to have an escort if you can just essentially shove them in a locker somewhere before doing a section? It makes things easier but also pointless, and it's not really something that I can ultimately consider a plus.
One thing that I do like is that unlike a lot of other NPCs, you can upgrade and also heal damage that Ashley might take. By giving her the same herbs that give Leon extra health and recovery you can buff her health up so that she'll be able to survive a couple of stray shots or scrapes that she might get into. The ability to at least give the person you're escorting a better chance of survival a battle is a good start to how an escort mission can actually be made more bearable; it also adds a strategic element: do you take the power-ups, or give them to the NPC, can you balance an even split, or take your chances by either buffing yourself to the gills or giving them the best chance to survive at the cost of maybe not being able to yourself when push comes to shove.
What I want to talk about now though, is a game that, to many, is the escort mission done right: Ico. I haven't actually played Ico -- although I do plan to pick up the rerelease double pack of it and Shadow of the Colossus -- but from what I've seen from online videos and just the general talk about it, it actually goes a long way to making the escort mission not only tolerable, but something memorable and lovable. To Ico's credit it does a lot of things right from what I've seen.
First of all is that both you as Ico and Yorda herself have no health. That is to say that dying in the game is incredibly hard. There is combat with the shadow creatures that want to kidnap Yorda, but these creatures can't directly kill either of you: the only way that Ico can die is by falling from a great distance (and the creatures will not hesitate to push you off one if you give them such an opportunity). Other than that it's only about keeping yourself and Yorda safe while you traverse the landscape. With no health to worry about and the goal of moving yourself and her forward it becomes less of a grind and more of a goal than simply keeping her safe for X amount of time while silently lamenting her existence.
One other huge thing that I've seen, something that puts Yorda above and beyond a lot of escorts in other games, is that she's actually helpful. If you're having trouble with a puzzle or don't know how to advance, Yorda is actually programmed to give you some hints to where to go or what to do. From a gameplay perspective it looks as if she's looking around the environment as well, trying to help you move forward because the both of you are on the journey together, and that's what people who are there for each other do.
I'll have to reserve more judgment for when I actually play Ico, but I have to say that I look forward to it as a rare example of an escort game done right, with an A.I. and playstyle that actually enhances the experience rather than detracts from it.