Yeah see I don't worry so much about this. I purposely follow people with whom I disagree (but who are well spoken) on Twitter to avoid ending up in an echo chamber. So I don't disagree with you about quashing diversity; the last thing I need in my life is to preach to the choir.
But the fact remains that, 1st Amendment or not, you can't yell "Fire!" in a crowded theater and then plead "but, but, my rights!" to evade responsibility. Credible threats are assault (look it up, it's in every state's legal code). I would not be surprised if doxxing was found to fall under similar statutes by an enlightened judge if done with malice aforethought.
Furthermore, an individual's rights to free expression do not include a right to make Twitter spend money or lose opportunities due to their chosen expressions. Twitter != the government. If push comes to shove, their self-preservation must take precedence (legally, since they have a fiduciary duty to their shareholders as a public company).
It's a chestnut, to be sure, but freedom of the press applies to those who own a printing press. Until and unless Twitter is nationalized (heaven forfend), they're restricted (at worst) by common carrier provisions. They can do a good job if it's in the best interests of their shareholders (and recent events suggest that may be the case). It's really an issue of how (how to maximize shareholder value, how to improve public perception, how not to drive away ads...).