Yes, I've heard Clarke go up to an F on his version of "Carnival of Venice," but it seems to be pushing the top of his range. My trumpet teacher, who was an orchestral player, peaked at about G. Even though the greatest old players may have had the chops to squeak out double Cs, it does not suit the style of the music. You notice that even jazz players who scream change their articulation and playing style for the upper register. It is extremely difficult to maintain an elegant style going that high on a regular Bb trumpet.
I don't think that Arban's compares aptly to the Bible, because it isn't a canon of all the most important works in that category. Rather, it is a book of fundamentals that every cornet/trumpet soloist should try to master. In that sense, it is more important that a cornet/trumpet soloist be able to play everything in Arban's than it is for him/her to actually play everything. You could argue, on the other hand, that a devout Christian really should read and know the entire Bible, although as Steve points out, it is often used as a reference book like Arban's. The point is that there is not much musical literature of great importance in Arban's. You might play a couple of pieces from Arban's now and then as a professional soloist but could still opt for an alternative arrangement.
Really, a classical soloist's "Bible" would be a compilation of all the great solo pieces that a professional would be expected to know well or at least polish to a quality level very quickly.