The question was:
Why would plants store their energy as carbohydrates and not as fats, if fats are a more efficient energy store?
But before trying to answer it you have to be quite clear what is meant by efficient. Without qualification this term is meaningless. A little reflection will tell you that whatever positive properties are implied by ‘efficiency’ may have different importance in relation to the very different modes of existence of animals and plants. One will also want to test any explanation on the exceptions — the instances where animals store carbohydrates (generally polysaccharides) and plants store fats. With this in mind I argue as follows:
1. Carbohydrate is the straightforward solution
Plants synthesize glucose from carbon dioxide, animals take in carbohydrates in their diet and break them down to monosaccherides. Hence, storing excess as polysaccheride (glycogen in animals, starch in plants) involves developing and using a relatively simple polymerization/depolymerization system. One would therefore assume it to be the default. The question is then, “in what circumstances is it advantageous to store surplus as fat?”.
2. Fat is a more concentrated energy store, so is used to minimize weight
Dull eh? But that’s the answer. The following extract from Berg et al. explains this clearly (triacylglycerol is the chemical name for triglyceride or fat):
Triacylglycerols are highly concentrated stores of metabolic energy because they are reduced and anhydrous. The yield from the complete oxidation of fatty acids is about 9 kcal g–1 (38 kJ g–1), in contrast with about 4 kcal g–1 (17 kJ g–1) for carbohydrates and proteins. The basis of this large difference in caloric yield is that fatty acids are much more reduced. Furthermore, triacylglycerols are nonpolar, and so they are stored in a nearly anhydrous form, whereas much more polar proteins and carbohydrates are more highly hydrated. In fact, 1 g of dry glycogen binds about 2 g of water. Consequently, a gram of nearly anhydrous fat stores more than six times as much energy as a gram of hydrated glycogen, which is likely the reason that triacylglycerols rather than glycogen were selected in evolution as the major energy reservoir. Consider a typical 70-kg man, who has fuel reserves of 100,000 kcal (420,000 kJ) in triacylglycerols, 25,000 kcal (100,000 kJ) in protein (mostly in muscle), 600 kcal (2500 kJ) in glycogen, and 40 kcal (170 kJ) in glucose. Triacylglycerols constitute about 11 kg of his total body weight. If this amount of energy were stored in glycogen, his total body weight would be 55 kg greater.
The animal exception — glycogen
A limited amount of fuel is stored as glycogen in animals. The increased weight load is offset by the advantage of rapid mobilization and the fact that glucose is obtained (animals cannot convert fatty acids to glucose).
The plant exception — oils in seeds
Plants do not walk around, so weight is not generally a consideration that would induce them to store their reserves as fat. They can develop large tubers under the ground, for example. However there is an advantage to minimizing weight in the energy reserves required for the development of seeds — it allows for easier spreading in the wind or through animal consumption. Thus one can rationalize why the energy reserves in seeds are oils (lower melting point triglycerides on account of their greater unsaturation).