Why can ATP not be stored in excess?
Let's compare ATP, glucose and fatty acids in terms of energy storage. 


ATP has a molecular weight of 507 Da
Glucose has a molecular weight of 180 Da, and contains the same amount of energy as 31 ATP molecules
Fatty acids vary in size, but a gram of fat contains about twice as much energy as a gram of glucose (or glycogen)


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"