...except that anything using finite resources is by definition unsustainable for the (long term) future
True, but that applies to everything. See:
Entropy and
Big bang to heat death.
Our problem is (will) be more along the lines of ever-expanding population making more demands on finite resources.
Even if we froze our technology where it is today, we can still deploy solar arrays which will provide all the energy we require, up to the output of Sol; see
Dyson Sphere.
I don't think we are running out of fuel, in fact we are are near to an "age of plenty". There is enough oil/Uranium/Thorium to tide us over to the point where we have fusion power - and if not, the Sun will provide.
If current scientific thinking is correct, we don't have an ultimate "long term future", so we might as well enjoy the present!