Yes, I agree that tu or vous are not marks of politeness but marks of social distance / deference.
That’s the reason why French people, regardless of whether they are polite or not, usually do not have to guess what to use. They know if the person in front of them is close enough or not and they remember if using tu was agreed in case the vouvoiement would have been the default usage.
What might confuse English people is when they are told using tu to someone you should have say vous is impolite, and using vous to someone you should have say tu is excessively polite.
They shouldn’t worry that much. This tu/vous ruleset is very relaxed when applying to non native speakers learning French. We are very lenient in that case just like we do not care about young children who say tu to everyone. They simply haven’t already learn to use the singular vous.
Switching from vous to tu is done either never or once, commonly after an invitation to do so from one of the parties.
Switching from tu to vous is extremely rare. Once you start saying tu to someone who doesn’t express disagreement, there is no reason to revert.
Your fight example is a case where this can happen but it is still a very uncommon kind of event. The switch is indeed done to put some distance again between the people involved.
Another case is people talking together at the TV or radio who switch to vous for consistency and deference. For example a journalist that say tu in private to an interviewee and vous with some others will use vous with all of them in public.
Indeed the use of tu/vous is a matter of social distance. A misuse of tu/vous becomes a matter of politeness because the appropriate social distance has not been observed.
There are many ways you can observe social distance in the choice between tu and vous. For example:
- There are a number of formal situations where people stick to vous even if they would have otherwise used tu with the same person. For example: in the army, in Parliament, in judiciary hearings, …
- Within a family, there is no social distance, so tu is the norm.
- The higher the social class, the more people use vous (even within the same class). Aristocratic and even bourgeois families used to use vous, but this is no longer practiced (or only by a select very few).
- During the Revolution, people started to use tu systematically, as a political statement: there are no social classes, so there should not be any marker of social distance between people.
- If two people meet in a dissymmetric situation such as a vendor and a customer, they will usually use vous. (Younger people might not, though.) The dissymmetry in the situation creates the need for social distance. If the same people later met again through mutual friends, they would use tu. At work, it depends on the company culture and the industry.
- People who see themselves as members of the same group tend to use tu. This applies not only to groups of friends, but also to social groups. People who attended the same school, who are active in the same political organization (at least left-leaning ones) or charity, or even who are members of the same sports club, often use tu, even though they would have used vous if they’d just met on the street.
Changing between tu and vous in a fight can go both ways. Changing to vous from the habitual tu can be a way to create some distance with the other person. Conversely, changing to tu from the habitual vous can be a way to breach the distance in order to stress the aggression.
Note that although French people choose intuitively, there are ambiguous cases where people don’t know which one to choose. It’s usually better to use vous when in doubt, because putting too little distance is worse than putting too much distance. However unduly using vous can also alienate people by putting too much distance. If you have a foreign accent, you’ll generally be excused. Natives will usually ask when in doubt.