Leaving the japanese term instead of using the english one we've always been using breaks immersion, when reading you aren't supposed to become aware the characters aren't actually speaking the language you're reading. That's why the terms in English were invented in the first place.
1. No, that's not why "trap" was invented. It was born as a homo- and transphobic joke about how people were "tricked" into liking men because those men looked like girls. It then evolved as a way of describing these "men" who look like girls (including trans women, both irl and online), which then lead it to become a somewhat common way of translating otokonoko, especially among weebs steeped in 4chan meme culture where the term originates from. Though it was never the only translation for it, mind you.
2. That's not how translation works. It's purpose is to convey the meaning of a text in the target language, whether it's done through extensive localisation or a large use of loanwords that may or may not be explained depends on context.
And the thing is, English has throughout history been quite happy to take loanwords when it hasn't been able to find an accurate native term whether it's from German, Latin, Greek, French, Spannish, Italian, even non-weeb Japanese like tsunami.