the damage calculations are being done right the vast majority of the time, and Riot works hard to fix the bugs that pop up. Death recap is messy because there ISN'T an easy way. I have 0 idea how much programming knowledge you have so I am just going to go over with the assumption that you know nothing about programming. Programming is messy, and hard, and about 40-80% of writing a program is fixing all the issues in it because getting things to work exactly as you want them to is a horrendous pain. I was not in any way joking or over exaggerating when I said a dedicated team working on tracking all the data would spend months on the project at minimum.
Your link isn't loading for me but I am guessing that it is something along the lines of "Fiddlesticks fear - 1k dmg" (something I have happen to me)
This is because trying to track all the data and permanently record it (for the rest of the game at least) would require so much ram that in estimation, I am guessing that Riot would have to set up a separate server system just to handle it. Of course then you run into the issue of having to send that data between the servers so that people can see their death messages. I am sure that there is a "simple" way, still horrendously complicated but doable without ruining the game for everyone playing, however that is the type of system that has to be built in to the central way league deals with damage from the ground up. It is basically so deeply embedded into how league works that over half of leagues code would need to be rewritten from scratch. That is not happening. As I said, I have 0 idea how much knowledge of programming you have, but as someone who works in programming on a daily basis trust me when I say that the amount of work required to do that would be... Idk, I am actually unable to find words at this point for just how big of a project that is. I would be amazed if league has less coding than skyrim and that took years to code without constantly releasing new things and bugfixing etc.
Maybe they will find a workaround and get death messages to be more accurate, but it won't be easy or fast even in the best situation. Riot isn't trying to withhold info, they just can't track the info itself after is runs through the programming.