Other countries have rules about political advertisement especially before elections. Those include budget limits, content, attribution, locations, and more. It's weird to think the rules are so lax here.
The Citizens United case, the most recent Supreme Court case striking down restrictions on political speech, was about a nonprofit organization opposed to Hillary Clinton. The government tried to shut down their “documentary” film about Hillary.
i.e., there is free speech for groups as well as individuals
Saying there's right to free speech for groups unless someone gets paid is a little silly and hard to enforce. Hence our current situation.
From another perspective, there is obviously "freedom of the press" but the Constitution does not say who is allowed to own a press and it doesn't say you have to personally own a press to make use of it. In fact, it would probably be problematic if you weren't allowed to hire a press if you had something you wanted to say.
Additionally, money is not speech. We disallow politicians directly giving people money to vote for them - why would we do that, since the politicians trade is in speech, he's simply delivering stump speech in the form of a $100 bill to his potential constituents.
And groups do have voting rights. That's how Congress works. The U.S. is a republic.
Not any arbitrary group gets to directly vote, no. But different groups do have rights: races, religions, genders, ethnicities, and, yes, groups of people with common values and interests.
Corporate speech is just "speech for groups of people". Those groups may be for-profit corporations, or they may be nonprofit.
Hate speech law in the US is practically nonexistent. Libel is much more difficult case to argue. Restrictions on political speech are widely held to be unconstitutional.
Compare that with other democracies, such as the UK, Germany or India, and I think you'll find that the US does have significantly more freedom of speech than other democratic nations.
Try, for example, to blog that your company should not trade with Israel whilst tendering for a federal contract.
(Just an example: I don’t have a dog in the actual fight).