I think it's actually false 99% of the time, because as soon as we get Y for cheap, we start consuming it more, and we are back to not having enough Y.
Also, this phenomenon is called the "income effect"[0]: as the price of a good Y falls relative to other goods, consumers' "income" will increase in a real sense (i.e. they'll be able to consume more of all goods), so they may increase consumption of Y, depending on whether Y is "inferior," "normal" or "luxury." The definitions of these concepts have to be made carefully to avoid circularity, but suffice it to say that 99% of goods are not normal.
Energy, however, is a normal good when measured, though a 2x increase in income leads to less than a 2x increase in energy consumption for a sufficient starting level of income. (If you were living in a remote village that was only recently electrified, for instance, electricity would be a luxury good: increases in income would lead to significant increases in consumption of electricity up to a certain point.)
What's more interesting is how firms react. Decreases in energy costs could lead to significant increases in productivity for firms, allowing for economies of scale that did not exist ex ante. This isn't really "consumption" per se, as energy is being "converted" into another good. But it seems likely that firms' demand for energy could increase quite a bit as the price for energy decreases.
[0] https://en.wikipedia.org/wiki/Consumer_choice#Income_effect
+in 70 years we'd probably have fusion
Strictly speaking, U-235 is the only fissile isotope of any element that is found in any significant amounts in nature. However, breeder reactors can also be useful. The only two starter points I'm aware of in nature for significant energy extraction are U-238 and Th-232. U-238 breeder reactors are politically complicated because they can relatively easily be used to generate significant amounts of Plutonium which is usable in bombs.
Th-232 reactors have technical hurdles that are probably surmountable; specifically the neutron economy is significantly tighter than U-238 breeder reactors (this is why you often see liquid-salt reactors proposed for Th; chemically separating the decay products gives plenty of breathing room in the neutron economy). The U-233 it generates is also usable in bombs, but since it will tend to also generate U-232, which is both difficult to work with and easy to detect, it's considered less of a proliferation risk.
This all misses my original point though. At any point in the first half of the 20th century we had enough oil to last us for centuries at then-present day usage. Yet here we are.