Just to briefly revive this topic, the reason I'd like to be able to access RStudio.Version is to extract RStudio.Version()$citation, so I can cite RStudio in any RMarkdown reports I create. Not just for reproducibility's sake, but because I want y'all to get credit!
I'm working on a little script that automatically includes a citation in the References list for every package used in a .Rmd file, as well as citations for base R and RStudio. Then this script would be run in the setup chunk every time a document is knitted. But currently, I cannot automatically include the RStudio citation in this way.