You illustrated the problem yourself. Usually when you are wondering what hit you, its not because you got crit, its because a bunch of shit all hitting you at once and very quickly. Thats something that a 'this hit kill you' death log will tell you nothing about and you'll still have a bad experience with a vast majority of the time. To have a true death log for it, you need the servers to have a running log of everything that hits you which is an incredible strain on the server given the large playerbase at league launches. It doesn't matter if the log is 15 seconds long or 2 seconds, its still logging everything that happens to your character at all times because you can die at any time. The only difference there is what it displays to you once you've died. The 'this hit killed you' log is just a bandaid on the problem, its not a solution, and you'll still wind up here complaining its not more in depth after it tells you little about most of your deaths.
Leon made a joke about 'small indie company' and while they might not be that small indie company anymore, the game still runs off the engine that was designed by 3 guys in a garage office who had never made a video game before. A real solution to this problem will have to wait for the new engine in PoE2.