The legal basis to intervene is there, but may be vague and open to interpretation.
For instance, a near-monopoly position might cause other regulations, like laws against unfair business practices to be interpreted more strictly than for other intermediaries:
https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:02...
As long as the population within a jurisdiciton univerally supports the principles behind a ruling, finding some regulation to support it usually can be done.
In the US, there seems to be two factors that make it a lot harder to enforce such regulation (to the extent that they even exist there) - The fact that these companies are American and able to buy influence through lobbying and contributions - The current division in American politics, where virtually any position supported by one side automatically will be opposed by the other, causing paralysis
> Only the most hardcore market fundamentalists/objectivits tend to disagree about this principle, in my experience.
Even if the court agrees in principle, it still needs a adequate legal basis to issue an order. Violation of a law, or a contract, or whatever. I asked the GP, who seems to have experience with such cases, what this legal basis this could be.