Because first amendment is to limit government power. Private companies are not obliged to give you right to free speech. In theory private companies compete against each other but government has a monopoly on legalized violence.
Whether a website wants to display tiktok or not is the same thing - it'll do whatever it thinks will get more users.
Now it is true commercial monopolies can also exert coercion on their customers, so we have antimonopoly laws. These laws likely need updates to deal with natural monopolies coming from the strong network effect in the internet era. And the interaction with free speech right in social networks will be an extremely challenging issue.