Will it? Part of Tiktok's genius is that you don't even need an account to view content, or even the app - the browser experience is quite good.
Now compare the friction between wanting to see a Tiktok right now, versus trying to see one of whatever Snap's equivalent is, or Facebook and Instagram's.
Maybe that friction exists cause western companies follow some pesky regulations about user data. And, they want to make sure they can monetize their content by blocking unlimited access to those who have not accepted their terms and conditions.
Maybe tiktok doesn't follow those to begin with...
Both TikTok and Instagram are banned in Russia, and yet people use still them. You're underestimating the “network effect”. (Is there a proper name for that?)
There's no reason to switch now. Ban TikTok and people will switch.