I doubt that we have extracted even 1% of the valuable, accessible non fossil resources of Earth yet, and while I know that the more valuable materials are also harder to extract, the moon is currently 100% unutilised, so the idea of near term war for resources on the moon seems like an extrapolation too far for me.

That’s not to say that there is no chance of war on the moon, given enough time as you say, but “enough time” IMO is centuries, at which timescale any kind of prediction is really just a guess.