Most bigcos aren't doing that because it's illegal, not because they don't want to.
If you, e.g., have market dominance in operating systems, you can't prefer any web browser, install any browser as default, or advertise any based on the OS. In the same way, if you control web search, you can't prefer one web shopping site, or one web maps service. And you especially can't integrate one, but not the other.
The goal of all this legislation was to ensure that a company like Google can't use their advantage in search to gain an advantage in maps, to avoid exactly the current situation.
It's not as clear cut as that. Someone actually has to bring the antitrust suit. In the last few decades, the US government hasn't been doing as much of that as they used to. Once in the suit, then you have to argue about the "relevant market" to determine which other companies count as competitors. This question probably consumes more time in an antitrust case than any other. Then you have to argue about how much of that market the defendant controls.
At least in the US, I know of no legislation forbidding a dominant OS maker from preferring some browser. Microsoft was put under some rules like that after their antitrust suit, but that's very different from legislation forbidding all companies from having such preferences.
Europe is different. I've not studied their antitrust law as I have that of the US, but I believe they're more aggressive on both the enforcement and legislation sides. I think the average American would be better off if US antitrust policy were more aggressive than it is now.
So you're saying that we shouldn't expect any new competition in web browsing, and it's expected to stay an Oligopoly forever, unless a new entrant to the market gets a significant advantage?
That, too, sounds exactly like what would be needed to demand more government regulation of that market.
One of the tasks of the government is to ensure that any market is free to new entrants, and that only the best product wins, and network effects are eliminated.
If you, e.g., have market dominance in operating systems, you can't prefer any web browser, install any browser as default, or advertise any based on the OS. In the same way, if you control web search, you can't prefer one web shopping site, or one web maps service. And you especially can't integrate one, but not the other.
The goal of all this legislation was to ensure that a company like Google can't use their advantage in search to gain an advantage in maps, to avoid exactly the current situation.