The Fairness Doctrine only survived the 1st Amendment because the airwaves are a public resource: each area only has one electromagnetic spectrum, and the sections of it that are useful for broadcasting are limited enough that not everyone can have a useful slice of the pie. As such, if you're lucky enough to get a slice, the government gets to have a lot more control than they normally do over how you use it. You're using something that belongs to all of us but only a few people get permission to use, so you have to do your part to serve the public good in addition to the programming you want to broadcast.

Cable has none of that scarcity, since we can have effectively as many cables in an area as we want, and each cable can be stuffed with more signal than the airwaves can, since you don't have to worry about whether any given frequency can pass through walls or buildings, just copper. Without that, the government can no longer justify dictating content.