Out of the loop

While data privacy is a concern, in my opinion the real fear motivating the government is the massive control China has, indirectly, through TikTok, over citizens' beliefs and culture.

As another comment pointed out, Facebook (and Cambridge Analytica) had an enormous role in Donald Trump getting elected. That is the kind of influence and power that shouldn't be in the hands of a foreign power (ironically, it's the kind of power the US has wielded for generations over many countries). And the US especially doesn't want China or Russia to have that power.

If China felt inclined, they very likely could push to have the algorithm modified to fit a particular agenda - say perhaps promoting a pro-China candidate - and most users would barely notice and slowly be drip fed posts that nudge them in a particular direction. People in power could start to lose that power at the behest of TikTok.

As many will likely point out, there's a good arm's distance between China and TikTok right now, as far as we know, but it's possible they are more involved than they let on (much like the NSA and Facebook) and could become more involved over time. It's a risk the government is unwilling to take.

A good example of what kinds of things can happen is when TikTok published a post to every US user with their congressperson's number, urging them to call them to protest the ban. I'm certain that scared the shit out of the US government and probably did more to force the ban down mid than anything else.