I don't think anyone on either side really knew with oil how things would go. Hindsight is 20-20, and one of the two camps was going to win with 100% certainty. It's not fully decided yet mind you, peak oil could still happen if people keep increasing demand for it instead of weaning away from fossil fuels. But I don't think that scenario is likely at all.
Really though, this is why I sort of stopped worrying about peak oil about a day after I was first exposed to the idea. It was a very absolutist disastrous sea-change phase-transition sort of scenario, and those are relatively rare in real life. (Well, at some level they are very common: everyone is conceived at some time and dies at another. These details disappear in aggregate.) It's much more common for equilibria that have been stable over decades to continue that stability, even if at slightly different locations. Lots of things are more expensive in our modern times than they used to be; somehow society has survived.
While I agree with your "sound economics" conclusion, I think that tapering demand was not part of the "peak oil" modeling.
The underlying assumptions involve no particular shift to the oil demand curve, whereas with improvements to other energy technologies (renewable energy, but also natural gas) we find that oil demanded per unit output at a fixed oil price appears to decrease with time. (The covid-related demand shock is of course not helping to bolster this curve.)
Why is oil special? Why not peak iron, aluminum, concrete, NaCl, or any or the myriad other things we consume? All of them are in finite quantities, not only oil. Earth has a finite mass after all.
Oil is as renewable as any other renewable resource. It's made from plants.
We're only at risk of running out of cheap crude mined from the earth with a positive net energy return at a low price. We aren't ever at risk of not being able to have oil.
It's an open question whether our access to cheap fossil fuel will outlast our demand for it.
A: Our business is running out of money we can no longer get any loans at any interest rate.
B: False. You're not running out of money or access to loans. You can still get loans as long as you're willing to put down more collateral in cash upfront than the amount you're borrowing.
I think see why you used a throwaway for this insight.
Oil has many uses besides as an energy source. Even in transportation, oil is still useful as an energy transfer system even if it isn't an energy source.
Net-loss energy systems are very useful. Fuel cells and batteries fall into this category. The latter has already begun to function as a replacement good for oil in the automotive industry.
This process of substitution is a cornerstone of cornucopian theory, as described by the famous Simon-Ehrlich wager.
It's not clear demand would evaporate, by the way. Right now we produce oil at a variety of price points - from cheap light crude at a few dollars per bbl to shale oil at ranges from $30-90/bbl. Most folks expect electric cars to undercut oil at higher price points. It's certainly possible we might some day develop technology to obsolete even oil at light crude extraction prices. But it's also possible that we would opt to produce petrol products in a net-negative energy process because petrol is just so damned convenient for energy transportation.
In a sense we already have, as Fischer-Tropsch can produce at around $40/bbl. We see it used today in special cases such as on aircraft carriers to work around logistical complexity. Producing jet fuel from seawater is very handy, if costly in terms of energy consumption.
Oil and oil products are very much renewable. The price points relative to substitution tech will change over time and some day we likely will decide that oil just isn't attractive anymore. Above, I suggested this might happen before we run out of light sweet crude (mostly from Saudi).
I think this is a very reasonable thing to wonder.
We use fossil fuels in fertilizer production because it is cheap. It is not the only alternative, nor are fertilizers required to operate at scale in the first place. Fertilizer increases yield but has nothing to do with our ability to scale an operation.
It's also important to distinguish between energy production and energy transfer. Petrol products are very useful for energy transfer even if they aren't energy producing.
Batteries and fuel cells are other examples of useful net-negative energy transfer systems.
Peak concrete is also sound economics, it just gets less air time because there are more alternatives and fewer affected industries.
Math please?
And remember when people talk about peak oil, they mean oil that is cheap enough to be of economic use.