This is just a comment but in community wiki format.    Most studies of semisimple 
(or reductive) algebraic groups and finite groups of Lie type emphasize counting the number of classes of various elements with a view toward representation theory.    So it's tmportant to consider *motivation* when counting elememts. 

Concerning references, much of this goes back to Steinberg.   A short summary of further work is given in my 1995 AMS book on conjugacy classes, e.g., section 8.9.
In spite of their misleading title, classes are the subject of a paper bu Peter Fleischmann and Ingo Janisczak <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=1212240">here</a>.    Note too Steinberg's theorem stating that the set of regular semisimple elements in any semisimple (or reductive) group is open and dense, consistent with your observation: see 2.5 in my book.