Some comps could easily be won with 1/4 & 1/4 but others you need at least 1/2 & 3/4 choke in my opinion, that's why multi chokes evolved, surely experience should tell you which combination is best for a particular shoot. As for shot string, it does not exist, it doesn't matter how fast you swing your gun across a pond and shoot, you will never see the mystical shot string in the water!
Shot string does exist there are plenty of high speed videos on the web showing it and some actually measuring the length.
As for seeing it in water you are correct, someone bothered to work out the maths for it once, you would have to have a gun swing speed of several hundred miles per hour and actually break the sound barrier to make a minimal difference that could be seen in water.
Basically, the shot leaves the barrel too fast and you could only move your barrel millimetres if that before its all left.
On the subject of moving pattern plates and shot string length, I remember reading an article about a Major Burrard in the 1920's shooting at a pattern plate that was on the side of a truck travelling 40 mph at a right angle to the shooter. It did move the pattern centre up to 5 inches at 40 yards.
Others have since replicated the experiment in modern times with modern techniques and done a bit more work on it.
The outcome was the length of shot string played no meaningful part in breaking targets. The difference in speed between target and shot means the target would have only moved a few inches before the whole string (even if it was a few feet long) would have passed any intercept point.
You also have to take into account effective shot string, you are always going to get a few pellets way out in front and a few deformed ones lagging way behind which elongate the shot string somewhat.
So, focusing on the entire 100% of the shot string (first and last pellet to hit) can be misleading. Focusing on the effective bulk of the shot can dramatically decrease the length of the effective shot string and therefore the amount the target clay moves in the time for it to pass.
99% of the time the shot hits the target rather than the target hitting the middle or tail end of the shot string (obviously the clay hitting the shot scenario can happen, just it’s a fluke rather than the normal way of hitting a target).
I’ve seen some interesting high-speed videos showing the shot string hitting targets on a skeet filed to back this up.
Unless you are constantly missing by a few inches at 40 yards the length of shot string isn’t going to help much.
The best I have ever shot (more than once) is with ½ ½, I do sometimes change to skeet for low driven or rabbits that are bouncing. But the best I ever shoot is when I leave ½ ½ or 3/8 3/8 in and don’t change, god knows why I bothered with 3/8 3/8 but I did and shot well with it so left it in.