I agree, but this is a subtle question.
On the one hand yes, there's no need for emotional display for its own sake. As far as I've observed, that is mostly a cultural (or really a subcultural) marker anyhow; some communities value it, that's fine. I'm not personally that comfortable with emotion as a tap that gets turned on and off on demand. (During the group I mentioned above, I told them that if they kept asking me what I was feeling, the only feeling they were likely to get out of me was anger about being expected to feel something.)
That sort of cultural practice is a different thing, though—completely different—from deep feeling coming into experience as part of a healing process. The latter is not a tap and there is no quality of display about it. It is more like a flood that rises from forgotten places, and the healing comes from surrendering to that flood and allowing it to change whatever changes. Maybe after that you become more emotionally expressive, maybe not; I personally think that matters less than people in these communities say it does. But you become more integrated, gain capacity, become less reactive, less conflicted.
The subtle part comes up when you say "Publicly?". Yes and no. I don't think there's any need for ongoing public emotionality. I do think there's a deep reason why healing can't fully happen in isolation. It's because our wounds happen in relationship, usually in early relational experiences, and what is wounded relationally can only heal relationally. Personally I have found that frustrating—I would rather go off somewhere, resolve my issues myself, be a self-healing organism. But I've come to see how this impulse to isolation is actually an aspect of the wound itself, and so not a way to heal. Wounds don't heal themselves—they just repeat until something changes. As far as I can tell, there's no way to avoid connecting with others if you want that to change. But others' mileage may vary, and in any case this connecting needs to happen in safe, closed environments with strong containers, not in random public settings.