So FINALLY i managed to get what Luis has been trying to tell me about the 4-beat kick all this time. Being a mathematician, I just couldn't understand how a 4-beat kick could make sense. If you have to coordinate the arms and the legs such that the pulling arm is on the same side as the kicking leg to facilitate rotation, then the only way to achieve a symmetrical 4-beat kick is to kick right-left-left-right, which doesn't make much sense. Luis showed me an incredible video of Sun Yang breaking the 1500m freestyle World Record, in which you can clearly see a 4-beat kick:
What is clear from the video is that it is NOT symmetrical. It is a combination of a half a cycle of a 6-beat kick on the side which he breathes to and half a cycle of a 2-beat ("Total Immersion style") kick to the other side. It means that there is a slight pause between each cycle of 4 kicks. It seems like it could be a good compromise for these kind of distances. According to a book I have on swimming, it says that studies show that taller swimmers tend to prefer a 2-beat kick as their longer legs would lead them to have too low a cadence if they were to employ a 6-beat kick, while more powerful swimmers with floatability issues tend to prefer a 6-beat kick in order to keep their legs up.
I think the point here is to have a kind of "toolbox" of different kicking patterns which you can reach into and use as appropriate depending on how tired you are or how fast you need to go to catch the feet of the guy in front. Even in a supposedly optimal performance like the one by Sun Yang in the video, you can see him seamlessly switching from one type of kick to another. He makes it look like second nature.