The three main dumps serve different purposes. The meat dump, which comes first, imparts its flavors primarily to the meat. The gravy dump, which comes second, provides the foundational flavors for the broth or "gravy" in which the meat is suspended. And what I call the kicker dump, third in the rota, adds the "brightness" and extra punch to the chili.
Competition cooks have used this method for several decades and arrived at it through much trial and error. I would trust them on this.
Blooming spices (cooking them in oil for a few minutes) is often done to add complexity to the flavor of a dish. This helps the flavors of the spice really open up. This technique is used quite often in Indian cooking.
Some spices can get lost if cooked a long time or can change flavor. This is why a recipe may opt to add seasonings towards the end of the cooking period.
Play around with the concept, look at lots of recipes and make notes of your experiments. I find Indian cookbooks deal with this concept the best.
Spices, including the chile powder, change character as they cook. Often spices added near the end are described as being 'brighter'.
Competition chili cooks talk about adding spices along the way, and think that this produces a superior product. I can't say whether you would notice the difference or not.