ngl, I feel like the term flat arc exists to cover up for failed character arcs
failed character arcs in the sense an arc was set up but didn’t reach that intended conclusion so there was no catharsis
and then people who like this character backtrack to remove this failed writing by saying actually this arc was never set up they were intended to remain as they were at the beginning
I feel like the term itself points to this phenomenon, flat arc is an oxymoronic and redundant term
an arc by definition is not flat, geometrically it is a curve so it cannot be a straight line and in narrative an arc requires change
we already have a term for a character that does not change, it is a static character
it is perfectly possible to have a static character as a protagonist but they’re typically confined to serials where the interest is not in being a character study
this is really obvious in detective mystery style stories, the detective often has a personality quirk rather than a character arc and each book or episode is essentially an anthology of crimes they solve the thing that is new and interesting is the crime not the detective changing
hell benoit blanc is practically a caricature of all these detectives and he feels flat and absurd inside his own movies, the characters with depth or verisimilitude are everyone else especially the female lead and the villain
this does not mean an arc cannot be applied to these characters, this is basically where the modern golden age of television comes from, characters who previously might not have received arcs inside a serialized television show might have been static as holding the status quo and familiarity is used to improve chances of syndication and longevity as well as just being easier to write
but the ones who receive character arcs that fail are not characters with flat arcs
if they received an arc then they did change and they are not static, being dynamic characters with an intended character arc does not mean that the arc is guaranteed to come out to be a good one, and if it does fail that does not magically make the character static and give them a “flat arc”, no they did change so they do have an arc it just wasn’t effective or thematically coherent change