In the rules as they stand (at the top of the page), there's nothing to prevent me from placing several numbers into one cell (in that I'm not disallowed from doing so)

In fact I could fill up every cell with all of the numbers 1-9 and I've completed the puzzle according to these rules!

At least one use of the word "exactly" ought to be there.

(plus, this illustrates the general need for an easy-to-understand visual example alongside any instructions we give - this, I'd think, is how almost everyone first learned how sudoku really worked)

Adding the caveat that each digit should appear exactly once in each of the constraints is superfluous information - which in my mathematical training has always been considered bad style.

In contrast to mathematics: In my educational training, giving the theoretical minimal set of instructions for people to follow is considered very bad style! The style guide for mathematics understandably asks us to omit unnecessary information, but in puzzling it's highly desirable to make the detail as clear as possible. (or suffer a lengthy Q&A session)

Having said all of that, Sudoku is a special case. My favourite instruction set would be:

"Sudoku...

you know what to do!"