However I use my own rstudio addon to View() anything in script, usually I assign ctrl+D to that feature so I just ctrl+D on anything in script (it can be an expression).
This is by far the most frequently used feature of my addon.
I tested again and found it works but with some limitations:
it only work with data.frame, while View() can also work on list. I found the list viewer to be one of the most useful new feature from RStudio.
if there is a function at same name, it will open the function definition instead of variable. In data.table usage it's common to name dt as the variable, which will lead to dt function with this.
it's single click so you cannot select arbitrary expression ( I often select a portion of a line to View it).
I knew you can press F2 to open function definition(didn't know it now work on data.frame), this seemed to be exactly same with F2.
For what it's worth, the limitation that only data.frame objects can be viewed will be lifted in RStudio v1.2.
Your other points re: choosing a data object vs. a function, and viewing an arbitrary expression, are good ones -- would you be willing to file this as a feature request, at https://github.com/rstudio/rstudio/issues?