When you want to run stuff client side instead of your server is one question to determine.

For R specifically, it is focused on stats/graphing. So if you wanted an app where someone could upload data and fit a complicated regression model, this would be a good use case. (There are probably javascript libraries for regression, but if willing to live with the bit of start up lag, worth it for anything mildly complicated -- factors in R for example would not like to worry about writing my own code in javascript to make the design matrix.)

In the case where you run the server, the data has to travel to your server, your computer estimates the model, and it sends it back. WASM apps this all happens client side.

It is a good use case for dynamic graphs/dashboards as well. If the data is small enough to entirely fit in memory, can basically have a local interactive session with the data and everything will be quite snappy (do not need to continually go back and forth with your server to query data).