IMO the main problem is the existence of an institution that is (arguably) more powerful than any government in the world.
That's not necessarily a problem on its own.
It becomes a problem when those same institutions have a very small number of people with specially concocted classes of shares that give people like Zuckerberg majority control of the company despite owning < 30% of actual shares.
I don't want to live in a world where 1 person can have such immense and unchecked power. Especially when that 1 person is immune from, for example, being removed as CEO.
I'm not sure if it's still the case today, but I believe Sergy / Larry had 51%+ control of the company despite only owning ~10% of shares.
Which is why the US government has been collecting all the data they can from google. It's a perfect means to perform mass surveillance on everyone and google has no power to refuse to hand that data over or even to tell anyone about it.
They only way I can think of to solve this would be to limit the amount of data that companies are allowed to collect, but can we expect the government to vote for that until google does start to abuse what they have on us? Right now they can take that data and benefit from it as well.
People are worried by their power.
Too much power is dangerous.
Google works at global scale, if even the US want to stop them from becoming even more powerful there must mean something.
If you think about it the NBA draft was invented to avoid that the best team chose the best players year after year
It's what you call "punish their success"
I cal it "enable competition"
Google is king of the keywords (products and services), Facebook is king of targeting (brand awareness)
But they are not really competing against each other on the contrary the gap is widening
Google made 61 billions more than FB in 2018 and 65 more in 2019
That's why FB is moving towards a marketplace based on their own cryptocurrency
Also, there's the issue of public trust. We have no choice but to trust Google not to skew its search results. It's not obvious this trust is justified.
Google can literally make individuals, companies, and events disappear from the Internet. You can put up your site or your business and if Google removes you from search you might as well not exist.
A moment's thought will suggest that this is exactly the same as the YouTube problem, but on a larger scale. And that's an unhealthy amount of power for a corporation that isn't subject to any oversight or accountability.