I also like very much simple approach, following principle KISS. However this will be too simplistic, just pin the shoulder. As in aikido there are no rules, attacker can do literally anything to go out of pin. That why I appreciate Michael and Kevin input, because their real life experiences follows similar 'no rules' scenarios. In this context, I like to think that from technical point of view the control of whole body structure is a minimum as opposed to concentrate on only one point of the body.
Real life experience tend to demonstrate that such control by one person can be achieved only with big difficulty and carries out a lot of risk. Nonetheless in aikido it is some kind of standard and it is approached as an easy routine.
But this discussion can give us some partial answer for question HOW.
Now, still we should ask question WHY.
Look around in real life and you will see the answer to you questions. Both how? and why?
You will see many hows and only one why. So if you want reality look in the right places.
Doormen might be a good place to look where they may be seen pinning someone. I'm sure you can think of other places where this may be a more common occurance and thus see various methods.
The why? I've already given in it's simplicity, to disable. To prevent from moving or escaping.
In Aikido that is the purpose yet in other arts it's may go that step further and the purpose may be to cause submission through pain etc.
I saw not too long ago a thief who was breaking into a car get chased down my road and caught and pinned. Bystanders called the police whilst the apprehended villain, although he couldn't escape or move could actually move his mouth, which of course never stopped ranting and saying how he was going to do him for assault.
Technically I would say the best formula in Aikido is first a control technique followed by a pin. Thus Ikkyo, nikkyo, sankyo etc. Thus to differenciate also between control technique and pin. For example sankyo may be hard to master but once you do it's a good go to control technique in 'live' situations. But once again it's once you are good at it which takes slow methodical practice.
From the ikkyo pin personally I don't rely on extra stretching and prefer just enough stretch but that is not the main thing. The main thing for me is having center over the elbow and it feels like you are sitting center on their arm. This type for me removes all struggle from the person being pinned.