A substantial amount of what people call "corruption" in American politics is instead two cherished principles of American society being fundamentally at odds as a result of our representative system. We want everyone to have an equal say in government, but we also want people to be able to freely express their political opinions.

Why is it wrong for an environmental group to be able to draft a proposed law to give legislators something concrete to work with? Why is it wrong for an industry organization, which usually knows way more about the specific industry than the lay public, to educate legislators about their industry? Why is it wrong for a rich person to buy media time to convince voters of his views?

These activities aren't inherently wrong. They're not inherently corruption. We might not like the consequences resulting from these activities. Often, we just don't like the people engaging in these activities. But as long as they're directed at convincing people (either voters or politicians), as opposed to giving out personal benefits, these activities aren't corruption.

You are not the first to notice this. What's your proposed alternative? Keep in mind that once money is spent, the spender no longer has it. If power is used, the user still has it. So it would be a bad idea to let powerful people have the soapbox instead of people with money.

Yes, but shutting it down smacks of censorship/abridging free speech. Or, at least, that's the argument that you hear.

It's an equality vs liberty issue. Either my free speech is violated because you have more money to voice your side, or my speech is violated because the government isn't letting me express my views by buying an advertisement. My point is that there is a tradeoff. Surrounding any different issue you have different people on different sides of the scale. i.e. you don't like the person buying the advertisement so it is undemocratic OR I am very passionate about the issue but the government won't let me spend money to advocate my position.