What does grow with demand is technological innovation and effort, and while we were not as close to the actual limit as we assumed with "peak oil", that doesn't mean the limit itself was fictional.
Yes, it is not physically infinite. But it is effectively.
As long as someone is willing to pay for it, it will be provided. And even cheaply - look, what's 1970's $12/barrel in nowadays dollars? $50? $100?
We are so nowhere near running out of oil, that the whole possibility is best ignored.
This is only true until it isn't. At some point oil will become economically and technologically infeasible and alternatives will win out, because no one wants the million-dollar a barrel oil economy that results when we have to resort to mining Titan for it.
And it will, but I fail to see how this defeats my statement.
Oil will become obsolete not because its price will rise, but only because the alternatives will finally become cheaper.
Which is not the case as of now.
The supply grows alongside with the price people are willing to pay for it. As you yourself pointed out.
Nowadays the demand falls, the prices fall, this would be followed by a fall in production. But whatever happens oil will be available at an affordable price because world just doesn't work without it. If oil gets too pricey, reserarch into digging up more oil more cheaply will be funded. As it happened with shale. And it will end up in one more oil price crisis same as the one we're witnessing. And the one after it.