I just learned that ATP can not be stored in excess and is only made by the body when it is needed. What makes ATP, like glucose and fat is what is stored under the skin or wherever. Now why cant the body just produce ATP and store it for heavy, heavy exercise when it would advantageous for it to be ready rather than it going through the production phase and then used. When I say ATP storage I mean in large amounts.
I think @AlanBoyd and @MadScientist have touched on the answer, fat is better suited by density for storing energy than ATP; ATP is optimal for quick conversion to bioenergy. Look at the question in another way: ATP in bioenergy cycle is dynamic - its an energy flux from food and breath to bioenergy.
Biological energy is used at essentially the same rate at which we take it in. The vast majority is used as soon as its available. If we were to try to store enough ATP for say an hour the costs would be large.
This back of the envelope calculation (see section 3.8) shows that 1 day of ATP is 64.5kg for a 2800 kcal a day energy intake. Approximately equal to body weight.
Of course ATP is stored in excess - just a few seconds worth though, 8 if you believe competitive cyclists. ATP is a pretty small quantum of energy... Even an hour storage would add 12 pounds to an adult body weight. That's a lot. And what advantage would this give us? We might be able to engage in high energy activities (which use ATP faster than we can make it) for longer. But up to now it looks as if improvements in efficiency in generating ATP have been adequate for animals to stay competitive.
Look at how evolution has dealt with the other component of bioenergy: oxygen. We can't hold our breath for more than a few minutes. 22 minutes is the current human record; impressive but still not that long. Oxygen is in plentiful supply brought in from outside and the adaptive costs to storing oxygen internally would simply not justify building up such a capacity for most of us. It seems even that aquatic mammals only hold their breath for a similar amount of time as we can if we practice. 20 minutes for Orcas. Penguins too. This isn't meant to be a survey of all animals ability to store oxygen, the point being that storage of oxygen has an adaptive cost that is not trivial.
Let's compare ATP, glucose and fatty acids in terms of energy storage.
The difference in energy density is huge, you would need enormous amounts of ATP to replace glucose/glycogen as energy storage mechanism, not to speak of fat. You can't put an arbitrary amount of ATP molecules into a cell, you 'll get into problems due to the osmotic pressure lots of molecules inside the cell would cause. Glucose is stored as glycogen in cells due to this effect, which makes one large glycogen molecule out of lots of glucose molecules.
The energy density difference is even larger if you take into account that ATP and glucose bind water, while fat is stored without surrounding water. The actual difference in energy density of glycogen and fat is around 6 times.
ATP is also not as stable as fat, it can get hydrolized in water. This would be a problem for long-term storage of energy.
You'll find some more details in Albert's "Molecular Biology of the Cell"
Not a complete answer, but a few random thoughts to start off the conversation:
1) There is another molecule that is used as a fast access store, and that is phosphocreatine which can be used to very rapidly rephosphorylate ADP in muscle. In resting muscle it is present at about 5x the level of ATP.
2) Levels of ATP are also used by cells as a regulatory input - in other words the fall in ATP levels with the onset of exercise triggers a response to replenish ATP through e.g. the breakdown of glycogen. In this view it is useful to have a final stage "energy currency" which can act directly as an enzyme substrate and whose level is a sensitive indicator of current energy demand.
3) ATP is also a substrate for RNA polymerase. If ATP was present at vastly higher levels than UTP, CTP and GTP it would probably cause errors in transcription, and might also interfere with the regulatory role of GTP binding proteins, since it would act as a competitor for binding at the GTP binding site.
4) In any case, if ATP was to be maintained at a much higher concentration for rapid use, presumably as soon as it began to be used the ATP generating systems would have to start up to try to replenish the pool. In other words things would really be no different from the way they are, but would simply operate at a higher resting level of ATP.