@sweet-potato:
It's a good question. As with many isekai, there doesn't seem to be a compelling reason. Normally I'd say it's to achieve a self-insert fantasy but that doesn't really get much mileage here, not with this painfully frustrating, hand-wringing romance.
I felt it did do some service as some dramatic irony. It does sort of go out of it's way to point out that, though they got along in the first pace because she's overly mature and a bit aloof, that same "maturity" is strangling their relationship as she always is making room for the mistakes he's making (rather than being young and having a healthy fight about it early on). Well, as you say, that much could be done without the isekai tropes, but the irony bites more when it's her very "otherwordly knowledge and character," which was supposed to be helpful, yet she is in fact shooting herself in the foot with.
Also, to a small extent, it makes her an "outsider," yet in a way that is distinctly orthogonal to her fiancee's sense of being an "outsider," which could be an interesting source of subtextual friction, depending on how you read it.
Beyond that, the only effect it has is that, just as with the demon-lord stuff and other stock isekai-y tropes, everything gets a slightly lighter overall tone (in that you get the broad impression you're not supposed to take everything
too seriously).