You actually want to burn the fuel quickly, you don't want to store the energy by pickling it or slow roasting it in the digestive juices for long times (your stomach is not a crock pot and first thing in the morning the metabolism is already in the resting phase). This is why the slow "complex" carbs -slow because they are harder to break down- are more likely to end up being stored as fat cells than "simple" carb sugars because the sugars will actually be consumed/burned/used up. Too much "sweets" usually is in reference to the cakes and cookies (heavy in the slow carbs as well as sugar). Otherwise one could get pretty fat by eating fruit alone. I think you only want to be doing the SLOW carb when the metabolism is up high enough to break it down and make use of it instead of tucking it away as fat - hence not for breakfast because you will have to expend more energy to process it unless you've turned up the heat first. But definitely a better choice at breakfast than for dinner before bed...
I would think of a fireplace where you can burn newspaper (simple sugar) or a cord of hard wood (slow complex carb) - which is likely to heat the room immediately and what debris is left over when the flame expires from each? In my experience the cord of wood rarely even burns to the inner core, leaving behind a charred and smoldering log, while the newspaper will leave only ash.
Err... well. You are mixing you apples with you pears. You have to understand that fat and carbs isn't the same kind of energy for your body and that it isn't used linearly, but parallely. Complex carbs is, unlike fat, still quite easy for the body to use. And the body can't store carbs as fat. This is a very usual misconception... the same way that very many people believes that muscles are "converted" into fat when you stop training, which is totally wrong. What appends is that the body stores the fat in the food as long as it has carbs to use instead since the carbs is easier to use. And the easier the carbs is to use the less fat the body use at the same time. When eating suger you body more or less tucks away ALL the fat that is in the rest of the food. If you eat a hamburger and drink a non diet coke all the sugar in the coke will make you body store away all the fat in the burger since it don't need to use it.
And if you eat NO carbs the body will use try to use only fat. This is how low carb diets work. You force the body to use all fat you eat instead of storing it. But it works bad since you need easier energy to be able to use proteins and fat in a good way. With no carbs in your body you will actually never be able to use up all your fat (look at someone really skinny that is on Atkinson diet and you will notice that they still have quite a high body fat percentage.). And also there is a lot of different body functions that actually needs carbs of other reasons... The same way that it needs fat, proteins, vitamins, and a lot of other stuff.
You would actually be able to loose weight after the same principle on a carb only diet. But this would be a even worse idea since you need fat to build new cells since the cell membranes is made out of fat and you would eventually die since your body can't build new cells.
The problem with eating fast carbs is that they are used so fast that if you eat them at breakfast you will not have any carbs left in the body long before lunch. This will result in that you body will try to use fat instead but since you don't have any easy energy to use for burning the fat you will get tired... and probably also get some cravings for sweet to replace does missing carbs which your body want to be able to use you fats.
By eating slow carbs in moderate amounts and NO fast carbs your body will burn both fat and carbs the whole morning until lunch. Also by eating full grain your body won't process all the carbs in the full grain since the human body can't process some kinds of fibre compositions.
If we take your fireplace example:
Fast carbs (suger) = paper
Slow carbs = kindling-wood
Fat = Firewood.
You can easily start a fire with paper... but its hard to start the actual firewood with paper only. And it's useless to use paper for trying to burn up everything of the firewood (You will have to throw in a lot of paper for a long time). This is kindling-wood much better for. It's not as easy to make kindling-wood to burn as paper... but it's still not that hard. But it's much easier to make the firewood to burn with kindling-wood. And it is almost the only way to actually be able to burn up all the firewood by throwing in some kindling-wood continuously (You won't have to throw in as much kindling-wood and not as often as you would have to do with the paper). And this is where your body differ from the fireplace (which isn't that strange since your body isn't anything like a fireplace.). In the fireplace you would be able to burn up the firewood by throwing in lots and lots of paper... but in your bode you won't be able to burn up you fat by throwing in lots and lots of fast carbs. If you do your body will just put away the fat and use the fast carbs instead. See it like if the fire would choose to use the paper instead of the firewood.