For a few players, pedal tones are more than a practice tool.  Claude Gordon's "Brass Playing is No Harder Than Deep Breathing" contains the following quote from an Los Angeles Times review of a 1905 performance by Bohumir Kryl:

"In triple Tonguing, in attainment of very high notes and in terrific coloratura work, Kryl is probably unexcelled in the world.  When he had shown off high notes, the people were startled at a tremendous low tone coming from somewhere--down, down, down it went, all the time coming, as you finally knew, from Kryl's magical cornet, until the notes would have registered bass on the scale, absolutely of deep trombone character.  How Kryl effects these notes, he himself does not know--they are of startling quality to anyone understanding the nature and limitations of a brass
instrument."

Here are a couple of quotes regarding the proper way to play the pedal tones:

Saint-Jacome, in his great method written in 1860, notes on page 81 the pedal "C" and states, "Existing on the cornet, to be obtained without moving the mouth, or LEFT ALONE."

Claude Gordon, "Brass Playing is No Harder Than Deep Breathing"--- "The lips do not play the pedals (they only vibrate) so do not try to play them by pooching out the lips or by other means of using the lips.... I have had hundreds of students, all of whom have mastered the pedal register."

"As a child, studying with Claude Gordon in 1959, I was told by other adult musicians that he, Claude (Gordon) could play the range of the piano keyboard on a Bb trumpet.  Naturally I asked Mr. Gordon if he could in fact do this.  When he replied in the affirmative, I unabashedly asked him to do it for me.  He gave me that little smile of his, took out his trumpet and double tongued his way down to the fourth pedal C below low C, and then in similar fashion up to a triple high C.  Needless to say, that made a believer out of me in regard to the Claude Gordon method of trumpet playing." -- Anthony "Tony" Horowitz, March 11, 1983.

It seems to me that using a separate embouchure for pedals would render them useless for performance, since you could not navigate smoothly throughout your range.

So, I guess this confirms what someone else wrote:  Double High C isn't really so high after all.  And Pedal C is not really so low after all.  I'm definitely a LONG way away from mastering this wonderful instrument!