The world's demand for energy keeps increasing because people in places like China and India see our lifestyle and decide they want to do the same.
The issue with fossil fuels isn't so much whether they can support us indefinitely, but whether they can support 10x that demand indefinitely. To which, even the Koch Brothers would probably say, 'No, they can't.'
In spite of hyped-up promotional material from their pipedreaming supporters,
renewables can't even replace our existing fossil fuel usage. (2% of world energy or 7% of electricity currently comes from wind and solar, in spite of massive investments in that area.)
So, we need a new energy source. Fast breeders, thorium LFTR or fusion are the only ones we currently know of that are capable of doing the job. Fast breeders have some horrific safety issues. So, that leaves the other two.