It does, especially given the name predates the country by 2-3 thousand years; it’s not exactly optimal but in reality “These Islands” is the only alternative and something is needed to refer to them from outside the islands.
Except it was a politicised term used by an occupying force to strengthen their claim over our lands. Apologies if the suffering of our people, decimation of our language and culture and not to mention crippling genocide should be tolerated by use because “British and Irish and isles” is too wordy for you.
Ill take south eastern icelandic archipelago if you would prefer.
It wasn’t, however the association with Great Britain is undeniable, especially when Lesser Britain doesn’t even refer to Ireland any more (in Roman times it did), but Brittany, however “British Isles” was in use by the Greeks (at least Prettanic Isles) before even that - well before the union of England and Scotland, never mind Ireland’s conquest.
Personally I’m happy with Atlantic Isles/Islands/Archipelago as I agree the term isn’t great due to the implicit association, but it’s not like it was something just made up by colonists.