>I'm not sure why the meme on the right is that the left wants to protect Biden or anyone else.

No, the point isn't "protecting Biden", it's pure self interest. Tiktok is a social media platform that's very popular with Democrat's electorate and is already left leaning. Why risk it falling into the other party's control (especially near the end of Biden's term), just so you can maybe push more left leaning talking points?