Not necessarily, because there's a ripple effect of conspiracy theories. They can damage people's lives beyond repair in so many ways. There are many, many people out there with twitchy fingers ready to pull the trigger on someone because they think they've been wronged by said person. I mean, Jan 6 has been painted as "Taking politicial prisoners" or "Antifa in disguise", "an FBI psyop", or what have you. The theory that the previous president had the election stolen from him cost a few lives that day, none of which matter to those who perpetrated said conspiracy in the first place.
At the end of the day, Twitter can still decide what they want on their platform and what they don't, that's their right as a private company. America is not the only country that uses Twitter, and wannabes have popped up as a result of "the death of freedom of speech" and yet failed for many reasons. Twitter is not essential to anyone, you don't have to use it. If you want to use it, you have to follow their rules. If I went into someone else's house and peed on the floor, what do you think they'd do? "Oh, it's your right to use my floor as a toilet"?
The greatest advocates for freedom of speech actually don't really care about the concept, they just want the right to say what they want without personal responsibility. Of course, if you said anything they didn't like... Then hot damn we're right back where we started. Freedom of speech is nothing more than a political platform used to drum up anger from those who want their voice heard, no matter how terrible that voice might be.
Think of your most loved person on the planet. Now picture some rando with a million followers on the net spreading conspiracy theories that they were engaging in some incredibly shady behaviour even though you know it's incorrect. But the mob won't have its mind changed no matter what evidence is presented to them and your loved one loses their job, their livelihood, and probably their life too if things got too far.
What these people want isn't freedom of speech, they want freedom from responsibility.
What you're saying is all good and well, if it were only one side doing it. But thats just not true. One side loves to censor everything they don't like/agree with, or label it as "misinformation." Who's the judge of what is correct or incorrect? What about when new information comes to light contradicting the wrongly labeled misinformation?
Your last paragraph happens far more frequently than you'd like to believe, but the left does it just as much if not more than the right. Look at Deshaun Watson. Not enough evidence to go to court, but thats not stoping everyone from claiming he's a rapist. Where is the misinformation label on cases like that? If twitter (and most other media) wants to be taken seriously they'd be consistent with the misinformation tag they love to throw around on right wing ideas.
We don't want freedom from responsibility, we want consistency. Either both sides can have freedom of speech or nobody does. This one-sided nature is complete and utter bullshit.