That happens, but it's far from the whole picture. When energy is cheap you grow a lot of low hanging fruit savings not taken that suddenly become worthwhile when prices rise. Market economy is ruthless about optimisation, and when a change from a wasteful process to a less wasteful process is even the tiniest bit more expensive to perform than just paying for the extra energy, then market economy dictates that it's not done.
Artificially increasing energy price can actually make an economy more competitive in the log run, when at one point in the future energy price will rise anyways. Even if we did not have any CO2 disposal problem, the era of fossil fuels would still end some day. Perhaps not even that far in the future, because imagine how much faster consumption would have risen in absence of any CO2 considerations.
Non-renewables are just that: not renewable. Discovering yet another deposit merely postpones the end, it does not change their finite nature. Will renewables eventually become cheaper than the last scraps of fossil fuel? Absolutely! Through both progress and supply quantities. But that's exactly what is happening here, "renewables before they were cool"
Categorizing sources into "renewable" and "non-renewable" doesn't change the math.
Centuries ago, our primary power source was lumber. Later it was coal and then whales and then oil. In the future it will be solar panels and fission and then fusion. The energy output of 1kg of fuel for a fusion reactor is many orders of magnitude more than what can be captured from burning 1kg of lumber.
And it's not a matter of "discovering a deposit". Hydrogen is the most abundant element in the solar system and in the universe.
Artificially increasing energy price can actually make an economy more competitive in the log run, when at one point in the future energy price will rise anyways. Even if we did not have any CO2 disposal problem, the era of fossil fuels would still end some day. Perhaps not even that far in the future, because imagine how much faster consumption would have risen in absence of any CO2 considerations.