Depends on the context.

Absolutely. The CEO's soft talk in your example is impressive because no one else dares to interrupt them. If you imagine a commision of dozen people, where one starts speaking with a soft voice, and is immediately interrupted by someone else yelling, and people show their agreement with the yelling person... that would send a completely different message about status within the group. -- To an outside observer, the first person could seem more sympatetic. But within the group, the second person is the winner, at least for the given moment.

There's a mind game aspect to it; for nearly any high-status move I can think of, doing the exact opposite is an even higher-status move (if you can pull it off),

And you can usually pull it off only if you have already accumulated enough status through other means. (I do X and conspicuously abstain from doing Y, to emphasise the power of my X.)

My model of a typical "people enthusiastic about fixing the rotten world" group is that most people there focus on looking good in the eyes of their peers. (If that actively harms the goal, most of them don't realize it. And if the world does not improve despite the effort of the group, that only confirms that the word really is rotten and the group is superior to the outsiders.) If you have very high status, you can afford speaking politely with the ignorant evil outsiders, because your peers know that despite your polite facade you truly despise them in your heart. But only a few members have status this high. Most people work actively on gaining it by signalling their loyalty to the group values, for example by yelling at people who disagree. And, for obvious evo-psych reasons, yelling at outsiders, especially the meek ones, when you have a full backup of your tribe, feels good.

(Note: Despite the tone of this comment, in the past I was a member of groups that tried to make other people see the light -- although I didn't yell at anyone -- and I was yelled at or otherwise shown contempt by groups who tried to make me see the light. In one case it was the same group, a few years later. I consider yelling and other forms of contempt unproductive when spreading ideas, but I understand the temptation of a monkey brain to do that.)

A homeless tramp yelling at every passerby is not high status.

Being a homeless tramp is low status. Said tramp using a social move that constitutes a status grab does not thereby change the principles of social dynamics.

Fact is, yelling can mean anything (an instance of the general rule that anything can mean anything).

This theory is worse than useless.

Talking with people politely signals respecting them, period.

Period? What happened to your 'general rule that anything can mean anything'? Is that the kind of fully general counterargument that applies only to your rivals, and not yourself?

What feels natural to you is a fact about you.

Non-sequitur one-upmanship.

You need a better class of friend.

Disingenuous and rude. You are attempting to distort Viliam's counter-factual illustration into a confession of weak social alliances. That would be untenable as a sincere interpretation of the meaning.