Seems like US regulators could just as easily decide that if the tech companies do anything really egregious the Europeans will smack them down so they don't need to do anything.
Let's take an example of Google being sanctioned and regulated for anti-competitive monopolistic practices abroad, but not broken up.
European or Asian (broad rhetorical buckets) regulations have no direct impact on US domestic regulations. Meaning that even if the EU held Google accountable they could continue to operate at home without changing their practices. While the argument can be made that regulation is likely to follow domestically I don't think that can be held as a truism under current geopolitical landscape.
Even if domestic regulations followed there would undoubtedly be a gap, during which companies would leverage that imbalance. Google would be pressured to make the most of its advantage in its shrinking monopolistic market while smaller companies would press their advantage abroad where they have better access to the market, investors, and customers.
Domestic inaction would be a net loss in the face of foreign regulation.
Thus the U.S. feels pressured to keep up.