The fact that they chose to shut down instead, strongly suggests, that they have interests in TikTok beyond financial.
I think it's more likely that they don't want the brand name dilution that comes from having a separate TikTok US that's probably going to be a shittier version of the original since it doesn't have the original algorithm (which isn't allowed to be exported) or the original TikTok engineers working on it.
Yes. At the time Larry & Sergey still ran the place and did have a somewhat idealist approach to running Google. When it turned out that it was impossible to bring an uncensored search engine to China, they shut it down.
Their Chinese variant of TikTok is called Douyin, so there wouldn't be any brand dilution from spinning TikTok off.
I also have doubts that the technology behind TikTok would be difficult for a western engineer to understand. It's a relatively straigtforward algorithm, and it's details have been shared in a public paper.
A financially motivated actor would have avoided the damage by spinning it out. They likely could have even kept a large minority share.