^^^^
Palmer and Kaminski address, slightly nearer the level of most of our heads, how chalk dissolved this way is very unstable in solution. It is quick to precipitate back out, on its own or by apatite reactions in the mash, and is also very slow to adjust pH (taking several hours to have anything close to the expected effect, which is reversible.)
I think all of us lay people can get an idea of how hard it is to get carbonate into water and how easy to get it out, even when it was dissolved under the uneproducible natural conditions of very high CO2 pressure over geologic time: We all know that just bringing water to the boil does the trick. But even more illustrative is that a simple drop in pressure, as from line pressure to atmospheric pressure, will cause it to break out of solution. That's how you get lime scale on a faucet. Surely I'd expect opening your 2 liter of Kai-style carbonated water would initate the process.
A.J. of course is one of their sources.
"Don't use chalk" is a very sensible rule.