Spend enough time in both continents and you’ll see that the proposition that the US is somehow more corrupt is not only disingenuous, it’s also probably dead wrong.
https://www.transparency.org/en/cpi#
This is only perception, but it's still pretty interesting and useful.
FWIW according to that the US is more corrupt than some European countries, less corrupt than others. You can probably even guess the countries that are less corrupt and more corrupt in Europe.
That's not remotely true. It is illegal to actually give any gifts to any government official (including elected officials). This extends in practical effect to "we have to charge the DoE for coffee when they're doing a site visit."
You can donate to political campaigns--just as you can in every democratic country I'm aware of. Candidates can solicit donations--just as they can in every democratic country I'm aware of. What's atypical in the US is that the party structure is incredibly weak (which means you get less relative funding from party sources, and therefore candidates have to get more funding from fundraising), and elections are so eye-wateringly expensive that you need to spend more time fundraising to be competitive.
If you get caught up in details, you won't be able to understand.
There are probably thousands of individual government regulations that each could cost AT&T more than $16 million per year. If lobbying was as powerful as some think, why don't they lobby even more?
Without lobbying, competition would have destroyed profitability of telecommunications.
America has no such restrictions. Members of Congress & the President start running & fundraising now ~2 years before an election (& unofficially before that). For the House of Representatives, that means members are in an electioneering & fundraising mode non-stop. The staggered election cycle in the Senate means that a large portion of the Senate is constantly campaigning further making focusing on the act of governing difficult. Fixing these issues doesn't solve all problems obviously but making no reforms isn't going to improve things either.
Not the OP, but ... murder or genocide is very clearly a crime, while lobbying starts with "talking to an elected official about laws that concern you", which is sorta normal in democracy, the elected officials should be available to talk. It only becomes problematic if it is overdone or done too secretively.
I think that a good and transparent lobby register is probably more useful than outright ban; at least an external observer can glean some information from it.
For the purposes of discussing government corruption, "lobbying" mean "talking to an elected official about laws that concern you, with the implication that their response will affect how much and in what direction you use money to pervert the electoral process". (Obviously, corporations generally don't actually explicitly say that part, because plausible deniablity.)
Lobbying is already legal, and is mostly a bad action; but if we make it illegal, it will create a black market that isn't regulated. It's the same problem (one of many) that the "War on Drugs" had, in that any activity that's illegal tends to be unregulatable. It also attracts to the market for people who are already doing illegal things.
I think the root of the problem is that politics in the US (and in most other places) is a popularity contest; it attracts people who are charming, lie effectively, and who's goal is to be popular. They, of course, have other goals too, but having the accolades of the represented is a requirement, and people that seek that status end up drawn towards politics.
The issue is under the first amendment, the government is not allowed to curb speech by people or organizations advocating for a candidate as a third party (which people can contribute to instead).
Of course, having a president who equates civil fines for late paperwork with criminal prosecution for dispensing hush money as equally benign "process crimes" is a major problem as well.
Unlike other developed democracies, the U.S. is a country where bribing the Congress is actually legalized, in the form of campaign donations. In fact, the main work of most congresspeople is to run after money to finance their next campaign. Therefore they will serve primarily the ones that pay them, not the ones that elect them.
When open source bribes politicians then they'll pay attention.