You're glossing over the difference between persuasion, which is protected, and bribery, which should never be. Money being channeled directly to elected officials should be heavily regulated. Today's campaign system requires fundraising, but it also (as we've seen over and over again) encourages influence buying. The sources of that money at minimum need to be disclosed so we know who is exerting their influence in the system.
How am I doing that? I am not advocating anything but the right of a person to anonymous free speech. Bribery is a criminal act, not speech. Besides, all politicians have to report campaign donations, and no one is allowed to donate more than $2000. (That is off the top of my head, I might be, probably am, wrong, but do not feel like looking it up.)
The reason Obama and others a demonizing the CoC is because they are in power, and trying to protect their seats. The only reason they want to know who is donating is so they can retaliate against the people who oppose them. That activity needs to be protected, unless you want someone to be able to demand that a cause you support that is unpopular with the powers that be face the same threats.
The simplest solution if we think someone is being bought is to kick them out of office.
Technically, but don't forget the strategic loopholes in the system like bundling and soft money.
How do we know if they're being bought or just as important, by whom when all individuals and their agendas have to do is hide behind a piece of paper and stay....anonymous? Can't act on information we don't have. And without knowing who the donors are, how can we determine whether their donation equates with influence?