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This is the same drawstroke I teach in my classes.

Like mentioned above, physics alone, the shortest distance from one point to another is a straight line. And this might work just fine if you're only throwing the gun out to full extension and only firing there. BUT, the key to shooting fast is getting the sights on target as quick as you can - afterall, you can't pull the trigger until your eyes can verify that barrel of the gun is pointing at your intended target. Therefore the quickest way to acquire a sight picture is to bring the gun straight up, rock with elbow and shoulder, and then extend out.

As soon as you rock the top of the slide should be in your lower peripheral vision of your dominant eye. For short distances (1yd or less) that's an aimed position and if your physical indices are good you should feel confident firing from this position (abeit your barrel might be aimed a little downwards).

After you've rocked the gun your support hand comes over and completes the "master grip" on the gun - again an aimed position.

Once the master grip is complete you can start pushing the gun out while bringing the gun's sights into your sightline. The important thing here is you don't want any excessive movements. Any extraneous motion has to be stopped before the sights are properly aligned - which takes extra time. Ideally once you pull the gun from the holster the only body parts that should be moving are your upper arm (rotating at the shoulder), and lower arm (rotating at the elbow). Keep the wrist relatively rigid so you're not moving your wrist and as your gun goes to extension you'll notice that your front sight will follow your sight line and the rear sights will just rotate up into position.

If a closer-range shot is needed (meaning breaking a shot somewhere between rocking the gun at the shoulder and full extension) then you can go ahead and a bend at the wrist. By inducing a third degree of movement (shoulder, elbow, wrist) you'l sacrifice a little bit of accuracy and stability, but gain speed. Besides, if the target is close enough that you need to break a shot before full extension then you don't need to be extremely acurate anyway. I've trained for a number of years like this and this is my level of comfort: 1yd or less - shoot after rocking just as the mizzle clears the horizontal, 2 to 5yds - shoot at 50% extension, 5 to 7yds - shoot at 75% extension, >7yds - shoot at full extension.

If you're going to use your gun defensively then don't train to always break the shot at full extension as you will do this in real life regardless of the aggressor's range. Going to full extension on a target that's 3yds and closing fast is a really bad idea and there's a good chance they're going to grapple with your gun hand. As the target closes in you want to draw the gun closer to your body and shoot from a more compressed position. You'll sacrifice accuracy, but gain speed. Defensive gun handling is all about balancing accuracy and speed to produce the shot needed on demand. IE: Taking a 25yd headshot on an active shooter may require maximizing accuracy (thumbing hammer back on a DA/SA pistol, deep breaths, perfect grip, stance, sight alignment etc) vs. taking a shot on a knife-wielding target 7yds out and going full-sprint towards you.

Here are some benchmarks I try to shoot for (no pun intended):
(Full concealed carry @ 5o'clock in a minotaur holster, closed front shirt - 8" circle accuracy standard)
Break shot after rocking gun horizontal: 0.8 to 1sec (1yd target)
Break Shot at full extension: 1.5 to 1.8sec (3yd target)