Power plant doesn't just mean fixed electrical generation plant. There's probably a gas-fired power plant in your car, for example. And you're correct that the main place fuel oil is price-competitive is in transportation, but that's less a story about cars and more one about the massive amounts of extremely dirty bunker fuel consumed by marine shipping vessels.
Even with electrical generation it's a mixed bag. The recent US fracking boom has also dramatically lowered the prices for natural gas. Natural gas burns cleaner than coal, so to the extent it's pushing us away from coal consumption it's serving to buy us some time. But it's still desequestering carbon, which means we're still going to need to stop well before we run out of available natural gas to burn.
Even with electrical generation it's a mixed bag. The recent US fracking boom has also dramatically lowered the prices for natural gas. Natural gas burns cleaner than coal, so to the extent it's pushing us away from coal consumption it's serving to buy us some time. But it's still desequestering carbon, which means we're still going to need to stop well before we run out of available natural gas to burn.