Why isn't it a long-term problem? As mentioned, we can use oil and oil products more efficiently and replace them with non-oil energy sources. Both of these tend to drive down oil prices. These suggest that peak oil isn't a real problem, at least in the world of high theory.
High oil prices encourage such efficiency and such substitution. This is what encourages the neoclassically-minded to see "market forces" as the solution. But there are other results of high oil prices, which do not solve the problem.
First, major political blocs exist which respond to high oil prices by invading other countries and the like. Thus, we see the US invasion of Iraq. This can actually cause oil prices to _go up_, just as the Nigerian rebels' response to being left out the oil price boom (by trying to get access to the oil) can cause oil prices to go up.
Similarly, high oil prices discourage such ideas as taxes on oil that discourage its use. Political blocs push for lower prices via political means.
Second, a period of low oil prices (which happens every decade or so) encourages rapid economic growth as measured by GDP and the like. Capitalist booms typically gain momentum and are hard to stop -- until they crash. The rapid economic growth pushes the world economy up against the wall of short-term constraints of the supply of oil, driving up oil prices. The growth's momentum means that this period lasts for awhile. Further, low-oil-price oriented technologies (SUVs, etc.) do not disappear from the economy overnight.
When the economy crashes, the resulting period of stagnation means that there is less of an incentive for businesses to invest in oil-subsitutes or even to improve the efficiency of oil-use and oil-extraction. Part of the problem is low cash-flow and profits. Part of the problem is that oil prices are low.
This period of stagnation sets the stage for another boom, another surge in oil demand and oil prices. The cycle as a whole creates a frantic mood that discourages long-term solutions, such as substitution and efficiency.
This is a very abstract picture, but so is the story of "Market forces" solving the problem.
Third, there's the obvious market failure: the true cost of using oil is far above the market price, since the use of petrochemicals simply encourages global warming and the like. -- Jim Devine / "There can be no real individual freedom in the presence of economic insecurity." -- Chester Bowles