Looking into the actual decision, it was based on extremely technical grounds - this specific regulatory measure is in violation of the rules passed by Congress due to a certain amount of ambiguity and sloppiness. It isn't the complete dismantling of regulatory authority that was feared, and virtually all of the power to regulate is still there.
It basically comes down to what Congress meant with "best system of emissions reduction" under 42 U.S.C. §7411(a)(1) that the EPA uses to determine the standards of performance promulgated to the states under §7411(d). Does it mean any kind of system such as generation-shifting (switching to cleaner power plants), cap-and-trade, and dare I say the Simpsons method, or is it restricted to technological means, designs, work practice, etc.?
Not knowing the legislative history, I gave §7411 a layman's cursory glance. I will admit the textual context is an air of technology, so I initially assumed it was restricted to the latter. Yet Kagan points out that Congress in 1990 amended §7411(a)(1) by stripping out
technological from the previous "best technological system of emissions reduction", presumably because Congress was worried technological means wouldn't be enough in the future, and I'll take her word for it.
Still, given the textual context, if Congress had intended EPA to have what amounts to legislative power, it would probably have been better use
regulatory scheme or
legislation instead of
system (assuming constitutionality of such a delegation of power). And the Clean Power Plan very much was legislative in nature. It effectively told e.g. every coal power plant to shut down, bulldoze the plant, and build something greener, which is a far cry from e.g. installing a CO
2 scrubber.