Order of importance is most important for argumentative essays. In building a persuasive argument it matters to put your strongest points first.

For example, if you are arguing in favor of bill that would reduce air pollution, a reader is likely to lose interest if you start off with minor points, such as reducing air pollution will help flowers in the local parks to thrive. Flowers simply are not that important to most people. But if you start with statistics about increases in major, life threatening diseases, such as cancer or heart disease, illustrated with the story of an otherwise healthy person who was debilitated by a disease related to air pollution, people are much more likely to pay attention. Once you have caught the reader's attention and presented your strongest case, you can then buttress your argument with less important, but still relevant points.

Rhetorical strategies such as description and narration don't have to worry as much about order of importance. Those modes can be very effective starting off in a low-key way and saving the more important points for the climax.

No. Order of importance is not used for all modes of writing. For example, if you are writing a narrative essay that tells a story, often using order of time is most logical. For example, if you are writing a narrative about how a person changed your life, you would probably begin chronologically and discuss when you first met that person, and work up to the climax of the story, which would be the event or events that involved you and that person; you would then mold that story into how the person changed you.

Order of importance would work best with Argument and Causal Analysis (cause/effect). Most likely you would begin with the least and work to the strongest so that your essay ends strongly. You may use compare/contrast with order of importance, but I think it would depend on the topic choice.

The answer I would give you to this question is a qualified yes.  Many writers use the most important to least important ideas while others use the opposite of least important to most important. For cause and effect, this works well, as it does for comparison/contrast or argument pieces. So that is true; however, that does not mean that these two are the only ways to organize especially if you include narration and description.  Sometimes it is more effective to use chronological order.  However, if your one objective is to emphasize which ideas are the most or least important, it is true that this is the way to organize.  I just would caution you that you must look first at what you are writing about and what you want to achieve.