However, I also also think trying to shut it down based speculative claims of being an intelligence threat are a bad idea and would set a terrible precedent.
I agree with that statement, but one must admit there's some hypocrisy on the part of China, given they have blanket bans on YouTube and Instagram which provide their own competing offerings. If China lifted those bans there could be no claims about TikTok enabling some asymmetric advantage in espionage or propaganda, and if they don't, China can't claim the US is doing anything they aren't already.
A good example is that google is banned but bing is not, and tiktok is also banned in China because they don't follow those laws.
This isn't too far from the US governments motivation to not have it's political power undermined by a foreign entity, and the propaganda situation is different between a democracy and an autocracy. It's politically impossible (and would be inconsistent) to ask specifically TikTok to remove all political content that could either bolster support from one party, or detract from another, as the US has the tenet of free speech enshrined in constitution. But instead of making up some nonsense law that social media companies must yield to coarse-grained censorship by the government, the US are at least being honest about their intentions.