Citizens United vs FEC is unrelated to what you are talking about. The court decision did not make contributions to politicians unbounded. The set ceiling is still in place. It did unbound the amount of money someone can spend on political speech that is not affiliated with a politician's campaign. You can donate only a set amount of money to a candidate that wants to breed purple lemons. You (or a separate group you donate to) can spend an unlimited amount of amount of money to advertise in favor of breeding purple lemons.
What you seem to be describing - disguising a donation from one individual to a politician that is over the contribution limit as several donations from different many different people - was and still is illegal.
Thus my "indirectly" modifier. A lobbyist cannot give $10,000 to the politician directly. They can give $10,000 to a PAC that is closed related to the politician.
The fund-raiser would also be legal. There is no masking of donations - those attending the fund-raiser do pay for their tickets. Nothing prevents a lobbyist from doing the legwork to make the fund-raiser happen.
Main point being, despite legal limits on direct donations, there are many ways a lobbyist can facilitate the flow of money from special interests into the pockets of politicians.
Your first paragraph is correct, people can give however much they want to spend on political promotion, advertisement, etc. That's what a PAC is, groups that organize advertisement.
You're still misrepresenting reality and when you say that this functions to "facilitate the flow of money from special interests into the pockets of politicians." This money never enters the pockets of politicians. If that happens, it is a violation of the law.
Definitely certain PACs benefit certain politicians over others. A PAC organized to promote environmentalism is probably going to help Democrats a lot more than Republicans. But it is not correct in any way to say that this money is funneled to the politicians themselves. The politician does not hold the purse strings of PAC money, the PAC can decide at any time to stop promoting items aligned with that politician.
What you seem to be describing - disguising a donation from one individual to a politician that is over the contribution limit as several donations from different many different people - was and still is illegal.