Well, if you look at the case that was in front of the court when they overturned Chevron: The National Marine Fishery Service decided that since the Magnuson–Stevens Act allows for them to place monitors on fishing vessels in order to prevent the over-fishing of certain species but since their budget was lower and they couldn't actually afford to pay the monitors they decided that each ship would have to pay for them.
The thing about Chevron deference is, it was already limited on its face: it only operated at all in places where the statute is silent or ambiguous, and only commanded deference to "reasonable" interpretations.
If the interpretation in Loper Bright was not "reasonable," the Supreme Court already had the tools it needed to reverse the agency without breaking any precedent. If on the other hand it was reasonable, why should the courts be getting involved?
Removing Chevron simply allows the courts to select their preferred policy outcomes more directly.
I am not a legal scholar, but from my understanding enough that serious cases were filed and fought and made in all the way to the Supreme Court.
In a https://www.scotusblog.com article, Amy Howe quotes the Chief Justice as saying "Chevron deference, Roberts explained in his opinion for the court on Friday, is inconsistent with the Administrative Procedure Act, a federal law that sets out the procedures that federal agencies must follow as well as instructions for courts to review actions by those agencies. The APA, Roberts noted, directs courts to “decide legal questions by applying their own judgment” and therefore “makes clear that agency interpretations of statutes — like agency interpretations of the Constitution — are not entitled to deference. Under the APA,” Roberts concluded, “it thus remains the responsibility of the court to decide whether the law means what the agency says."
I ought to go read the decision for myself, which I have to this point not yet done. I am not an attorney, but do have a general interest in these matters.
But back to the earlier poster's notes, ATF has been a prime example. They have a history of capricious reinterpretation at the whims of whichever administration is in power. They issue letters to people and businesses that say one thing is okay and then outlaw in without any law changes a decade later. I have never owned a pistol brace, but they stated it was an acceptable innovation for certain applications, thousands and thousands of people relied on that, they issue a rule making comment period and get feedback and then threw all of that out and came out with a final rule that bore no resemblance to the one in the comment period. Then they stand behind Chevron that the courts had to listen to their interpretation. It is legal "heads, I win" and "tails, you lose!"
In terms of 'applying their own judgement' I wonder if this would take the form of agencies still pursuing their normal course of regulation, but courts having the option but not the obligation to defer to that regulation as an expert reference, at which point they are essentially reifying the regulation into case law. I wonder if you'd even get cases designed to lead judges to rule for a regulatory agency's interpretation to get the regulation more firmly established.