It will not happen in our lifetime, possibly not our children's lifetime. But I think eventually the prices will converge.
can show you documentation of newspapers predicting the end of oil that occurred in the early 1920s. They were all ridiculously wrong almost a hundred years ago and are wrong now as production and reserves are larger than ever and continue to grow.
I have seen some articles that say we have not even scratched the surface for hydrocarbon production as a very small amount or just a couple of percent of what is found so far has even been produced, and Far larger amounts are yet to be found.
The only convergence can occur if the govt continues to intefer with the natural market for energy production, which makes energy more expensive for everyone.
Why even worry about these things so many generations from now?