The overruling of Chevron is not about stripping power from federal agencies, it's about determining who should resolve ambiguities in regulations. Should it be the agency itself, or should it be the branch of government whose job it is to "say what the law is"?

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.