To some extent, ByteDance doesn’t have much choice. China recently instituted new rules on AI exports that would require the company to obtain a license if it sold the algorithm to a US firm. Given that China would supposedly prefer to see TikTok shut down than sold off, that’s not particularly likely.
It wouldn’t necessarily be the end if TikTok lost its algorithm. It could develop a new system. However, there’s no guarantee the company could keep running in the US before that new algorithm entered use. If so, there might be a dark period where users would have to make do with other social networks.