Firing as fast as possible harms your kiln, or at least will wear out the kiln elements.
I believe this comes from the days when ceramic kilns were commonly used. Certainly this is still the mantra among ceramicists today.
A number of people fire their kilns as fast as they can, especially small ones, all the time. Refractory fibre kilns are not affected at all by rapid changes in temperature.
There might possibly be some small damage to the light weight refractory brick used in glass kilns in that the frequent expansion and contraction may cause crumbs to fall from the brick. But this will happen anyway as the brick expands and contracts the same amount every time it is fired. There is no definitive information on whether rapid increases in temperature have any greater effect on brick than slower increases.
Any rapid change in temperature is unlikely to affect the kiln elements. Attempting to bend the elements while cold is very likely to break them, as a compound is formed on the surface which makes them brittle when cold. But this is very different from rapid changes in temperature. As an analogy, the elements in electric fires are made of the same material and are always heated as fast as possible from cold. They have a long life, so there should be no difference in effect on kiln elements, which are generally thicker and less exposed to drafts and rapid temperature changes once hot.
It could be said that firing as fast as possible would reduce the stress on the relays in the controller, as they will be closed for the whole of the temperature rise, with no opening and closing. Thus, the number of firings will be increased without equally increasing the number of cycles the relays have to perform.
However rapid rises in temperature affect the kiln is secondary to how it affects the glass. Except for small pieces, extremely rapid rises in temperature increase the likelihood of the glass breaking. This is the more important consideration when thinking about afap firings.
All myths have an element of truth in them otherwise they would not persist.
They also persist because people listen to the “rules” rather than thinking about the principles and applying them. It is when you understand the principles that you can successfully break the “rules”.