Non-anonymous free speech is a bit of a red herring. If you say something publicly, especially in this era of mass data, you are perpetually liable to be punished for it at some point in the future. If not by the current government, potentially another. Virtually every country in the world has experienced authoritarianism at one point or another, and there is never a guarantee that it won't again. Saying something publicly tied to your identity is signing up to be imprisoned when an authoritarian who doesn't like what you said seizes power. We have many historical examples of dictators rounding up and executing wide classes of people, so we know this threat model is more than just a hypothetical but rather something that can and does realistically happen at various times and places.

Therefore, in practice, anonymity is the only way to safely express oneself in public. Privacy is the true bastion of the freedom of ideas. This is naturally lost when the means to communicate privately are stripped from us, when every word we've ever said is recorded and tied to our identity. Age verification could possibly theoretically be implemented in a way that does not immediately infringe upon privacy, but you surely know that there is no world in which it will ever be implemented in such a way.