Private companies are not obligated to offer services, and in the US the government cannot compel private companies to do so (except rare circumstances). "We will stop offering services if X does not happen" is not coercive, it's an ultimatum. Companies should not be expected to operate in a market hostile to them.
What about privatized utilities then? What prevents e.g. electricity or phone companies from shutting down when they don't like some rules? It's a little more nuanced than "all or nothing".
Losing TikTok for a few hours or a day is perhaps going to make TikTok users more angry at the government than TikTok.
Losing electricity or phone service for a day is going to make people more angry at the utility or phone company, regardless of why the shutdown has happened.
And if a utility threatened to shut down service instead of complying with a new government regulation, you can bet the government would immediately jail anyone involved in that decision.
Covered under "except rare circumstances". Regulations for utilities, telecommunications, transportation, and financial services are the exception and not the rule.
Because it's endlessly profitable and very low risk to run a utility, the company's board is... unlikely to ever decide to do a stunt. For what payoff?