PlayPump failed, as so many others, because children do not make good horses. Countless projects in many fields have attempted to "harness" children for energy. There was the soccer/football generator (https://www.youtube.com/watch?v=oeb2fyHKirQ). I've even seen attempts to install power-generating floor tiles in English schools (https://www.youtube.com/watch?v=_9AZxB55xjI). We think we can tell children what to do, use them as beasts of burden, but they are not a reliable power source.
The problem with the Matrix is even with made-up physics, they did a terrible job writing in humans as a power source into the plot. That's a fairly low bar and they failed.
It is claimed that in the original script, humans were used as a computing resource instead of an energy resource, but the idea was scrapped because it was too complicated to understand.
A bit like lovemenot next to here indicates.
I think it's a better and more terrifying plot if you watch it as a Kafka-esque dystopia where people are imprisoned by the machines for inscrutable reasons that no-one truly knows. Morpheus's power supply theory is then just a necessary rationalization and a part of the mythology that allows the resistance to continue, while being fundamentally incorrect.
Thermodynamic impossibility is a relatively minor obstacle for a true believer.
Me too. I always thought it would have been better if humans' processing cycles (thoughts) were utilised to supplement, validate and expand the Matrix. A sort of automatic, involuntary, unaware Mechanical Turk.