That being said, I don't think Chevron deference has a part to play when it comes to Net Neutrality flip flopping all the time - these are not ambiguous regulations. In that sense I don't agree with the person you're replying to - Loper Bright won't help here. Now, if you want to say that the FCC doesn't have the authority to issue this rule, that's something that was always reviewable by the courts.
The concept that would actually attempt to strip power from agencies is the nondelegation doctrine. While I suspect that has support among a few justices, it would be a very radical change and there is no case on the horizon that I'm aware of that would be a vehicle to implement it.
If Loper Bright had been decided ten years ago we would already know today whether the FCC possessed this authority or not and it would be settled. Instead, we are about to embark on another round of litigation because the FCC just unsettled expectations again.
Case 1: agencies reinterpret the law ever four years in each new administration until the end of time.
Case 2: we figure out what the law means once and apply it going forward until Congress changes it again.
Case 2: Waiting until every single individual aspect of every single law is litigated means for years to decades the actual meaning is ambiguous until each court case finishes.
This is an unbelievably slanted and misleading description of the lawsuit. The lawsuit is about stripping federal agencies of the authority that Congress has vested in them, shifting power to the courts. It's an attempt at a judicial power grab, nothing more.
For starters, your claim that "we never get a definite ruling on what the law says" is categorically false. The agency's rules are law. Changes in the rules are no different from Congress passing laws and then repealing them, something which happens all the time. (Agencies are actually more predictable than Congressional legislation, because they are required by law to broadcast proposed changes well in advance and solicit input through a formal process, something which Congress does not have to do.)
There is almost no universe in which this lawsuit, if successful, would "increase consistency". Instead, we'd get even more ambiguity, because the law would be "whatever a court decides", something which is not knowable until a lawsuit is filed (and sometimes even then).
That ambiguity is, of course, the exact motivation of the people backing this lawsuit in the first place.