You asked about "spread" lips and except for Clyde, no one have said anything.
James Stamp used to instruct the use of "hop" or "up" at the end of the inhalation just before starting the sound. Why? Well according to his students J.C. Wiener, Roy Poper or Mario Guarneri, this helps in closing the lips before starting the sound (buzz) and making the embouchure more effective.
A lot of amateurs (and others?) tend to set the embouchure without this "up", they have an opening between the lips when setting. When the air hit the lips it opens more and get too wide or spread for the desired pitch. The result is that the sound has no ring or body and it tends to be flat.
This bad habit not only manifest itself in a flat pitch and a non projecting sound, it also makes the embouchure inflexible (see Clydes point "the moving embouchure")
On page 40 in Philip Farkas "Art of Brass Playing" he has an illustration
of the aperture for 3 octaves (low F, middle F, high F). In that illustration
he shows that the aperture for the next octave (above) is half the size
of that below. Farkas says he has tested this theory on many players. How
he did the testing he does not tell, but I suppose he used a mouthpiece
visualizer. This statement (that the next octave is half size) is not always
true as Farkas says. A central factor here is volume.
Farkas says: "The highest, softest note one can play is the result of the smallest lip aperture he can produce". (And vice versa for the lowest loudest note.)
In his books "Maximizing Practice" Mark Van Cleave uses this "theory"
in his exercises (see text on page 24 in Volume I)
Here is a some of what he says:
"If you play louder as you ascend, you limit the embouchure's motion. The effect of the register you are playing will cancel
the effect of the volume you are playing. The embouchure just sits there. Motionless. The only thing that is being practiced and developed is your ability to force air. You are not developing a strong (controlled) embouchure, just a strong gut".
If one look at some of the "spread" lip players one can observe this
"gut" usage when they try to play in the upper register.
They have no real aperture control and they have to force notes with air (and strong arm).
Let me finally quote Malte Burba (it was my last post about him that
caused your question, Sian):
Air flows across the closed lips, which increases air pressure until the lips open. The resulting fall in pressure causes the lips
to close again. This process is then repeated, as many as thousand times a second.
Pitch is determined by the frequency of the opening and closing motion per second; loudness by the size of the motion."
"Oulee the Gentle Viking"