The reason why the arsinh transformation is useful (and this is not mentioned in the link you posted) is that it is the optimal variance-stabilizing transformation [1] under the assumption that your data is contaminated by a mixture of additive and multiplicative noise (the same way that the log transformation is the optimal variance-stabilizing transformation when your data is contaminated only by multiplicative noise).

Read the Wikipedia article for a more formal explanation.

[1] https://en.m.wikipedia.org/wiki/Variance-stabilizing_transfo...