I'd like to give an answer that interprets functional analysis broadly, not as simply Riemann analysis, but as a way of understanding harmony by examining how chords "function" and flow into each other diachronically.

But first let me speak like a linguist. In English you have loanwords from Latin, like data. But they are not grammatically treated like Latin: most English speakers will say "The data shows" instead of "The data show" even though data, in Latin, is plural. A Latin speaker, attempting to study English, might conclude that English "lacks" the grammar of plurality. But we know that that's not true; it's just that English's grammar is different from Latin's, and there's no law requiring that English obey Latin grammar when it incorporates Latin words.

A responsible linguist, then, won't be beholden to the idea that "data is plural, so if it's used as a singular, something is wrong." Instead, linguists have to make sense of the language as it is.

In the same way, functional analysis, as practice by modern theorists, seeks to be descriptive rather than prescriptive. In Classical music, V chords typically cadence to I chords and so on in the way you've described, and if you want to teach someone to write Classical music, you can prescribe that chords should follow those functions.

But even as pop music clearly borrows many harmonic concepts from Classical music (like building triads on each degree of the major scale), pop also has its own harmonic grammar, one that doesn't necessarily conform to Classical notions of functionality, but this doesn't mean they aren't functional—clearly each chord has a role or function to play in its context!

I'd like to give an answer that interprets functional analysis broadly, not as simply Riemann analysis, but as a way of understanding harmony by examining how chords "function" and flow into each other diachronically.

But first let me speak like a linguist. In English we have loanwords from Latin, like data. But they are not grammatically treated like Latin: most English speakers will say "The data shows" instead of "The data show" even though data, in Latin, is plural. A Latin speaker, studying English, might conclude that English "lacks" the grammar of plurality. But we know that that's not true; English has plurality, but English's sense of plurality is different from Latin's, and there's no law requiring that English obey Latin grammar when English incorporates Latin words.

A responsible linguist, then, won't be beholden to the idea that "data is plural, so if it's used as a singular, something is wrong." Instead, linguists have to make sense of the language as it is. This is called descriptivism.

In the same way, functional analysis, as practiced by modern theorists, seeks to be descriptive rather than prescriptive. In Classical music, V chords typically cadence to I chords and so on in the way you've pointed out, and if you wanted to teach someone to write Classical music, you could prescribe that chords should follow those functions.

But pop is not Classical music. Even as pop music clearly borrows many Classical harmonic concepts (like building triads on each degree of the major scale), pop has a unique harmonic grammar. Pop harmonies don't necessarily conform to Classical notions of functionality, but this doesn't mean they aren't functional—clearly each chord has a role or function to play in its context!