As just one example of what we're talking about, let's take Ireland: after generations of cultural oppression England caused a famine in Ireland that reduced the population by at least 20% between millions of deaths and millions of immigrants. Ireland still hasn't recovered its population to the pre-famine levels.
The Irish are literally still recovering from their abuse at the hands of England. They speak English because England made it so through generations of deliberate cultural extermination. It's unreasonable for you to dismiss their desire to not identify themselves with the British flag as some "type of PCness".
It's possible to just do "English" but sites are typically going to either do British English or US English. Not putting the British flag to avoid offense is just hiding the fact that you're localizing to British English to try and avoid offense. (Which doesn't actually seem better to me.) Unless you actually do separately localize to Irish English. But also why not just provide the same text under two flags?
Also, on the other hand, China may get very cross with you if you refer to Taiwanese Chinese at all. How you refer to a language is inherently political, and hiding the flag changes the political statement you're making, but it doesn't eliminate it, nor does making a consistent decision like "no flag" mean you're going to consistently side with oppressor or oppressed.
This is all "types of PCness" and I don't say that to dismiss it or say that I would never do something for the sake of PCness, but mostly to say that throwing out flags seems like a cop-out and not addressing the problems on a case-by-case basis.
The bigger problems are probably countries with indigenous native languages that only exist in that country but are also a minority... many Latin American countries where you might put Spanish with that country's flag but there is Nahuatl or Quechua or whatever. But on the other hand realistically you are only localizing to Spanish, so again, you're just trying to pretend like you've made a neutral political choice by hiding the flag.
At some point you just have to own the fact that you are who you are because of your history. An Irish dialect of English is still English and it still has that connection to the past, flag or no flag.
More importantly, Ireland speaks two languages, English and Irish. The Irish flag should probably be Irish language since English has other representations. But it isn't obvious.
I don’t see the need to upend this for some notion of offense or other type of PCness.