I promise, this is the result of real constraints! Monte carlo is used because of the limitations of analysis when using log-normal distributions. Normal distributions can be summed algebraically; log normal distributions cannot.
Note that Monte-carlo is not used prominently anywhere on the site, just here because I thought HN would find that part of the implementation interesting.
It is true that there is no closed form expressions for the sum of two independent log normal distributions. However, like I said, good approximations exist. Moreover, if you were to ask me to compute some expectation E[f(X)] where X is the sum of independent one-dimensional log-normals, it seems simplest to convolve the densities and simply compute the expectation by trapezoidal integration.
I think I misled myself into thinking your selling point was the technology (Monte Carlo), whereas as you say there is little about that on the website. And your comments below are right: building the tool around MC affords you a lot of flexibility without having to be increasingly clever.
The only thing I would worry about then are events which have low probability but potentially very high "weight" in whatever measure of risk you are using. Sometimes the weight can be so large that your MC estimates seem to converging, and then the addition of a single trajectory completely blows up your variance. These are related to the "black swan" events people sometimes talk about. I don't think this is a problem in your model.
https://blog.vistimo.com/post/169546687605/estimation-math
Note that Monte-carlo is not used prominently anywhere on the site, just here because I thought HN would find that part of the implementation interesting.