What's the point in choking enemies in Metal Gear Solid 4?
If you're playing at The Boss Extreme difficulty level and want to do a complete non-lethal run, you will find that the number non-lethal rounds you can carry are very limited and you cannot by them from Drebin. To save them for tougher situations like boss fights, choking 'smaller' enemies is one of the method.
Also, should I even bother playing the game non-lethally during my first playthrough?
If you feel it's too hard, just do a lethal run first. Then if you want to give yourself more challenges, go gradually from easy non-lethal run to The Boss Extreme non-lethal.
Is there any way to permanently keep enemies down without killing them
One way is to do a hold-up in crouch stance (crouch behind the enemy without being noticed, when close enough, equip a weapon and point at him/her [L1 then R1]), then press R1 without moving the Left stick to grab the enemy, after the grab, release and tap R1 while moving the Left stick to any direction, then do an hold-up again. If you success the enemy will lay on the floor face down and will stay in this position unless you trigger an alert phrase. But there are some areas in which this method does not work, mainly the war zones where the PMC and militia are actively fighting each other.
am I playing the game wrong?
Nope. Lethal or non-lethal, it's all up to you. But there exists some rewards which are available only with non-lethal finishes. One of them is the Solar Gun (awarded by finishing the FROG fight and BB fights non-lethally and get the figure they left), which is a very powerful non-lethal weapon and an essential one for getting the Big Boss Emblem.