Suppose that controlled fusion power requires real-time control computations which can be much more efficiently implemented in neurological hardware than in silicon.
(That Second Law of Thermodynamics thing was bothering the hell out of you, wasn't it?)
Note that neurological hardware really is exceptionally power-efficient for certain classes of computations. Common estimates of the human brain's power consumption are 20-25 watts; this is roughly the wattage of a Mobile Intel Core i5 processor, which (as far as we know) appears to be a much less powerful computer for many purposes. By contrast Watson runs on 90 IBM Power750 servers, filling ten racks, whose power draw is something like 80 kilowatts. In other words, Watson consumed about four thousand times more power than either of its meat-based competitors.
Here in reality, I think it's unlikely that any fixed class of computations can be efficiently implemented in neurons but not in silicon — see Carver Mead and his academic descendants' work on analog silicon circuits. But positing that such computations may exist seems within the realm of acceptable science-fictional handwaving.
UPDATE: Yes this is close to the standard handwave that the humans are being kept as computing devices, not power sources. But I think you need to draw the connection explicitly to power generation; otherwise there's just too much narrative in the film and animated shorts that makes no sense.
UPDATE': Never mind, I just remembered Morpheus's exact wording from the first film's voice over and I don't think it's salvageable. Oh well.