It's like forcing everybody to eat lettuce in a restaurant because some clients are on diet. It's horrible.
So I think a slightly different analogy would be that it's a restaurant for dieters, and with each drink/food-item, they give you a running tally of how many calories you've ordered.
Ie, if you want to eat at that restaurant, clearly you want a diet focused dining experience. They also provide you with a tool to monitor your calorie intake.
Likewise, a forum which bans users over civility is clearly one populated by people who seek that. Angry internet voices would clearly be unhappy there, and would not even want to take part. Likewise, that forum also could give you a tool to monitor how un-civil you're being, to help you stay civil.
The tool that I spoke of would be an aid to people already choosing to take part in that experience.
This would all be a very different story if it was forced on everyone who wanted to say, use the internet. I think your example would more closely resemble a police state. Unwanted rules, shoved down your throat.
IMO, analogies are fair game, and a useful tool for simplification. They can also work well for highlighting hypocrisy, when a supposedly universal rule is not being applied as widely as we thought it was.
There's nothing wholesome or 'meaty' about vulgarity. It raises the temperature of the argument and doesn't contribute useful information. It's more akin a diner pouring pig slop on a restaurant table and insisting that it's the other patrons' fault for finding it impossible to eat in those circumstances.
I think it is just as important to take things at face value, instead of assuming malice, as it is to be sensitive to other people's issues (for lack of a better term). I've actually had decent results debating obvious trolls, just by postponing emotion, identifying and avoiding assumptions, and focusing on the actual meaning of their statements.
I'm referring to resorting to crassness on an already contentious topic. As an example, I often spend time defending my religious beliefs to atheists. I'm happy to talk all day about how I feel about Dawkins' arguments and the like, but the second someone brings up 'your stupid f———— sky fairy', I can tell that the conversation is not going to be productive any longer.
(Side note: "Rhetoric" isn't a dirty word, or at least it wasn't originally a dirty word. In the classical definition of the term, rhetoric based on facts and cool logic was also possible, and was also considered rhetoric. The modern usage of "rhetoric" to mean exclusively "empty" or purely emotional argumentation is not what the classical politicians meant by it, and not how the term is used in an academic context.)
Therefore, it's probably impossible to keep the heightened emotions out of debate without strict rules on content and participation. The extreme end of this is Usenet-style moderation, which means every comment to a forum ("newsgroup", or "group", in the Usenet parlance) is sent to a moderator's email address to be specifically (usually manually) approved, and no unapproved posts will appear in the group. That kind of moderation has existed since the 1980s, but to my knowledge, no modern web forum moderates that way. Take it as the far end of what's already been tried.
That kind of strict moderation can look like content-based or viewpoint-biased filtering (as in, all messages with a specific content or which take a specific viewpoint) due to a simple founder effect: If the few people who want to discuss this topic, or take this viewpoint, happen to be intemperate, they get moderated away, and it looks like that topic or viewpoint is being moderated away. The forum gets a reputation for that kind of filtering, and it can be very hard to shake it.
Now, are there topics or viewpoints which are inherently inflammatory? That's another question.
History proves this, long before the advent of digital fora. Consider the elaborate, stilted parliamentary procedure and its variants. While it's quite burdensome, it's also considered a total necessity in many of the great deliberatory bodies that stand today.
Even with such a ceremonious structure, fist fights in national parliaments are by no means a thing of the past.
I think that this is because more than persuasion, humans are emotionally driven to create in-groups and out-groups, and only by divorcing emotion as much as possible can any real reasoning and discussion take place.
If there's one thing that profanity and vulgarity is actually good at, it's forming an in-group, which is antithetical to good discussion.
Those very definition are the first ones to be used (followed by "think of the children") as reason for righteousness, censorship and other politically correct legacy.
The point of free speech is to ensure that unpopular political opinions have room to air, everything else is a happy side effect.