Congress gives federal agencies the power to make policy choices for good reason: legislators are not technical experts and will never be able to write laws with specific technical details.

If Chevron is overturned and agencies no longer have that power, then who will make policy decisions? The courts. And as Sotomayor pointed out during questioning, since justices “routinely disagree” about a law’s meaning the courts will find it impossible to agree on a “best” interpretation of a law.

Yet courts will have to make those kinds of policy decisions anyway. Or tell legislators to rewrite the law, which they cannot do because they're not technical experts.

But not all Chevron decisions involve highly specific technical matters. The case that's before the Court now doesn't, for example. Federal law expressly allows the agency to require fishing boats to carry monitors - but it doesn't say who pays for those monitors. The agency said the industry has to pay; the industry disagrees. That's not an issue that's beyond the technical capabilities of either the courts or Congress. That's not a complicated technical question - it's not even a scientific question at all, but a pure public policy question. Arguably the issue in Chevron itself (whether a "source" within the Clean Air Act should be considered as a plant-wide thing, or whether changes to or additions to parts of the plant were sources) wasn't an especially technical issue, either - certainly one that was within the capabilities of Congress to legislate.

Legislators have to write laws on technical subjects all the time, and they have access to technical experts to help them manage that. Courts have to rule on technical subjects all the time as well, and the parties to the litigation provide technical expertise to the court to help them manage that all the time as well. And agency heads pretty much have to do the same thing - most of the heads of EPA (for example) haven't been scientists, but have been lawyers or lobbyists or other government folks who have skills at managing a large government organization but aren't themselves technical experts. And even an EPA administrator who is a scientist (say, a chemical engineer or an air quality researcher) is still going to have to rely on other experts for all the other fields they have to regulate (like water quality or fisheries or wetlands species preservation).