Apparently the largest solar installation in the world is used to generate steam that is used to extract oil. I can imagine (just about) a strange future with a renewable powered oil industry, because oil has certain benefits that electricity doesn't (use as airplane fuel for example). Such fuel would have a lower carbon impact overall, though probably only slightly lower.
I think it makes sense that at some point we'll start leaving oil in the ground, but not sure if that's because its price will keep going up, or if its replacements will keep getting cheaper/better, and what affect that has on oil prices.
Using renewables or nuclear power to extract fossil fuels amounts to something almost like indirect energy conversion/storage. It can also work between fossil sources. I've heard the tar sands described as a massive indirect gas liquefaction plant -- it's economical because direct GTL is less efficient than gas -> steam -> bitumen -> liquids.
But price spike/crash is something to pay attention too, in any field. Absent graft no one make bank on anything for too long.
This may or may not mean that the price of oil will go up forever in nominal dollars. It may actually have the reverse effect at times, since it could trigger financial crashes that result in deflation. It may also lead to replacement of oil with other resources (gas, electric, etc.) or shifts away from oil-based transport (electric trains, walking, biking) -- and those could lead to decreases in oil price as well if they occur to enough of an extent.
The error in predicting eternal oil inflation is threefold:
(1) Assuming that financial cost always reflects objective physical cost -- that there is a 1:1 relationship between thermodynamics and price. Reality: there's only a soft relationship subject to the next two factors.
(2) Assuming infinite demand inelasticity. Reality: increasing oil price fuels substitution and demand destruction.
(3) Forgetting that money (especially fiat money) is itself variable in value. Reality: deflation can cause prices to nominally fall when nothing has actually changed, and inflation can cause the inverse.