@Ferrum1I disagree, but for a specific reason: it depends on the story. Some stories are just fine with a small, limited cast - indeed, that's the best thing for some.
When writing on a large canvas, though, it rapidly becomes impossible. For e.g. a high school coming of age story, one has at minimum: protagonist, protagonist's S.O., parent(s), and protagonist's S.O.'s parents. That's six. One could water down parents a bit, but they're pretty important to the development of protagonist and protagonist's S.O., in my opinion. Then you have friends (one assumes), perhaps a significant teacher-mentor or two, etc.
Eight-ten and we've barely scratched the surface.
One can argue over what a 'main' character is, but the point is made.
Make that story long-form and the number of name-check characters is going to get very high.
It's not just SOL epics that have this problem, though. Steven King's 'The Stand' has at least twelve main characters, and that's being quite ruthless on who's a 'main character'. 'A Song of Ice and Fire' aka 'Game of Thrones' has far more than that.
I will, however, agree considerably with:
Nothing worse, imo, than introducing a new character and then having that character serve no purpose in the story except another piece of ass.
Unless, of course, the plotline at that point involves the main character being shallow and treating new people like a piece of ass - then there's a point. Also, any character introduced and treated that way is by definition not a first or second tier character, I'd say.
Not sure entirely if Chekov's Gun applies, though. One could argue that the construction "If a character appears in the story, they must wind up having sex" is analogous to "If a gun appears, it must wind up being fired" :)
One last thought: what constitutes a 'character'? For instance, I have teachers who appear virtually only as names. We've never heard them say anything, we don't know what they look like, etc. Are they 'characters'? Or 'placeholders'?
I have a paramedic who's appeared twice and had a bit of dialogue. He's important to the scenes he appears in but has no actual bearing on the story; some other paramedic with a different appearance and attitude would barely move the needle. Is he a 'character'? If so, what 'tier'?
Sometimes you need people like that to move the story along.
Then, we have people in classes with two dozen other students, and in the case of Drama or Debate, all of those other students are 'doing something' - acting or competing. Never name-checking them seems wrong, but many are third or lower tier. People aren't invested in them, and shouldn't be - but their names come up. It's not unexpected for readers to say 'Wait, who's again?' when X is the quiet freshman my main character sees literally every school day but interacts with seldom (but not never).
At the same time, my main character is unlikely to say 'X, who's usually just a quiet freshman, did really well ...' It's comparatively difficult to re-introduce X whenever they turn up, because from the first-person narrator's perspective, of course everyone involved knows who X is.
Thus the need for a CoC. It's not for the first or second tier characters. If you're forgetting who they are (even if there are quite a few) there's a problem. It's for the minor-but-name-checked characters who turn up every so often.
Also, in a long story, minor character X might well suddenly become a major character. Perhaps the quiet freshman studies and learns and suddenly isn't so quiet and is kicking ass. Or asks the main character to Sadie Hawkins. Or ... whatever. One of the fun parts of stories is that people's roles aren't always set and static.