First of all, this applies specifically to racing. Not to discount high performance skiers, but it's different. There are several things going on, and I think they need to be broken out a bit. First you can easily start the turn too early, and doing so will make you late. I know this seems counter intuitive, but draw a course on a piece of paper, set a fixed arc size with a compass and draw some "turns." Starting the turn too early can cause a lot of problems -- body too close to a gate, double turning, etc. When most coaches tell an athlete to start the turn earlier, really what they are saying is end the previous sooner, get off your edges and have a proper transition. Second, higher is not the same as earlier, higher is higher. Since the minimum turn radius of a ski is relatively fixed, the only way to tighten the line and allow ample time for the next gate/turn is to move the turn up the hill. I used to use early and higher somewhat interchangeably until some of my athletes started taking a line where the turn was too early and too low. I have to admit, I didn't know that was possible until I saw it. Last week, one of my athletes was nearly in tears because she was so slow in a slalom course. In reality, it was the fastest slalom run I had ever seen her ski because she skied a high, tight line. It felt slow because getting on that line, her turns ended earlier and she had more time between gates. When I showed her the timer, she was convinced it wasn't working properly.
As to the question about whether there are times that an athlete wouldn't want to be as early as possible, it kind of depends. It is very easy to over ski a course and take a safer line than is necessary. Also, while being late is never good, it isn't always bad. When I inspect courses with younger athletes, I try to point out sections of the course where staying on a high, early line is more important than skiing clean, and sections of the course where if you get late it is better to ride it out and not panic/where skiing clean is more important than being on the line.
As far as pressuring the ski earlier in the turn, I'm not sure about that. You want to get on the new edges as soon as possible, and you need some pressure to bend the ski into the arc, but by and large pressure happens from a little above the fall line to a little below it. Watching men's GS is a bit weird because what you are seeing is world class athletes trying to make skis that don't really work do something they don't want to do, but you will see pressure only in the fall line.
So how does this apply to skiing outside a course? It really doesn't. For general skiing, early pressure is fine as long as it doesn't prevent you from developing edge angles, but you can't continue to develop edge angle after the ski is pressured (try it). I see a lot of skiers try to pressure early and never fully developing edge angle. If you are in a strong body position, the ski will get enough pressure. For most skiers, it is easier to over pressure than over edge.