Don't think of it as having to have it absolutely straight after the apex. The literature does exaggerate it a bit. In a hairpin-type corner that you've posted a picture of your turn-in should be a bit later so the most steering is done at initial turn-in well before the apex, and the you unwind.
The intention is to have most of your steering done before the apex. In a kart you actually hold almost the same amount of steering angle all the way from initial entry to the apex. In a car there is usually more of a gradual increase of steering input and more of a gradual decrease on the exit. This is because in a kart the aim is to have the inside rear wheel lift - when it does the kart turns nicely and there is no need to dial in much more steering input.
When you start exiting the corner you definitely don't want to be steering more. If that is happening it means you've choked the exit (if you didn't dial in more steering you'd run off the track). The problem with steering more after the apex is that you can't possibly keep accelerating if you're also steering more. You end up creating understeer (because you're asking for your front tyres to turn more than they can at the speed you're trying to go) which often quickly snaps into oversteer.
I'm not that good at putting this into writing. Here's a video that shows how the technique effects your corner exit. I hope you're a Schumacher fan.
http://www.youtube.com/watch?v=f7Hoqw0oHdg#t=1m38sThe video should start at about 1m38 in, and from there until 1m50 pay attention to the track use at the corner exit.
Notice how Schumacher hits the edge of the track a full kart length or so later compared to the other drivers? The other drivers have to put in more steering input when they get to the edge of the track because they would run out on to the dirt if they didn't. Schumacher on the other hand makes it to the edge of the track a lot more gradually, and doesn't need to put in a lot of steering input which would slow the kart down when it's supposed to be accelerating hard.
Schumacher is the only one that isn't choking the exit. The driver right before Michael and the next 4 drivers actually make a real mess of the exit having to steer quite violently near the edge of the track.
