But now I'm wondering what percentage of the useful thermal power in a nuclear power plant is produced by the neutrinos created in the reactions (the infinitesimally small fraction that happen to interact with the matter within the reactor, that is).
But it's still just a single tiny particle, so it's not a lot of total energy.
It's like how you can lift a heavy weight for a second, but that's all you can do. You would need to be able to lift it for hours to be useful as a replacement for a crane. Same idea: Intensity vs total work.