Just to add some nuance, this seems to imply everyone has the same environmental psychology. There are lots of (often competing) perspectives. If you have a utilitarian environmental psychology, you may think resources are there to be consumed for human benefit. If you instead have a stewardship environmental psychology, you may feel its your duty to protect those resources from being pilfered.
Stephen Kellert has a good description of these different perspectives in "The Biological Basis for Human Values of Nature". Some of his categories include: utilitarian, naturalistic, ecologistic-scientific, aesthetic, symbolic, humanistic, moralistic, dominionistic, and negativistic. Other researchers define the human-environment interactions differently. For example, [1] defines them in terms of master, apathy, steward, partner, participant, and user. So it's not hard to see why people's thoughts differ on this issue. Like with most human value systems, it's not likely that there is a singular "right" perspective.
[1] https://www.academia.edu/download/53480185/Yoshida_et_al._20...
That's not really the logical conclusion of my advice. In actuality, there's a lot of possibilities between "I'm the one buying it, so I'm the only one dealing with the consequences" and "Not use any oil at all". But I get it, it's easier to argue against strawmen.
It's also easier to feel smug and accuse people of strawmanning when you're engaging in motte and bailey :^)
Accusations of fallacy aside, what is your actual argument then? That there's some non-zero harm inflicted on future generations when we consume fossil fuels, because they won't be able to use them anymore? That would seem like the motte argument, because it's trivially true, but what does this translate in terms of how we should behave? A cost of $0.000001 would be trivially easy to defend, but also means I can turn my thermostat to 78F guilt free.
You also argue that we've "we've got the externalities of climate change all wrong", implying that the future generations not being able to use fossil fuels is somehow worse than people being displaced by climate change today. What is your basis for that?
What's the point of resources if they're not consumed? If we follow your advice to its logical conclusion, then we'd have oils that are consumed by nobody, because every generation doesn't want to consume it for fear of "cost [...] borne by future generations".