The theory is that this is just one guy. He can introduce all the legislation he wants but requires over 200 others to also be on his side. A judge, by contrast, holds unique power in the room (or at least, one of a very small number).
In fact, given the difficulties in trying to reach a 60 vote threshold in the Senate, which has become essentially mandatory, the odds of this legislation going anywhere are extremely low. If it gets anywhere at all, it will be subject to the votes of the rest of the Congressmen, who have to face reelection.
Corporations can push to elect candidates who are predisposed to be favorable to them. They can't fund campaigns directly, but they can put out advertising to influence those voters, but voters are subject to a lot of influence, and it's easier to get other Congressmen to say "no" than "yes".
I'm not trying to defend the system; it's obviously a damn mess. But it's also the essence of representative democracy, a fundamentally antagonistic system. Judges aren't supposed to be in an antognistic relationship; they're intended to seek balance while juries make the actual decisions. (The top-level federal courts do work antagonistically, and that's actually a disaster in the making.)
You can't have legislators drop out due to conflict of interest: "interest" is what they were elected to do. The voters are supposed to be the brake on that: no matter what corporate push they get the voters can still dump them if they don't like it.
Whether the voters will actually do so on an abstruse issue like the FCC... well, there's democracy for you, and I have no further comment.