I had no idea about this, but that has been my head-canon for about 25 years now. The idea that the machines needed human brains for specially-biased RNG, creativity, emotions, advanced pattern recognition, or anything else AI tends to lack, just makes way more sense. But electricity clearly isn't one of those.

So Morpheus holding up a microchip instead of a battery would be no less poignant and, IMO, would absolutely be understandable by a broad audience. It also has a kind of dramatic symmetry that is way more poignant.

The battery theory is explainable by bad intel from the machines, humanity coming to a bad conclusion on their own, or Morpheus dumbing reality down for his recruiting speech. The last one fits well considering that he's talking to someone that thought he/she was living in the past, prior to the invention of artificial life. Saying something like "you're like the battery from your Walkman" is close enough to get the point across.