What’s most damning to their argument is that they’ve all acted within common-carrier boundaries anyway for most of broadband’s existence, with very few exceptions, and they continue to make record profits, expand service (mostly), and increase speeds. Common-carrier regulation would simply prevent some very harmful “innovations” that the ISPs have, to date, never needed to remain profitable and keep expanding.
Don’t believe their bullshit. They’d be perfectly fine as common carriers. Almost nothing would change from the way they’ve always operated.