@criver It's not a lack of brain, telling the government or not telling them are both valid and risky choices, it all comes down being selfish or not.
Telling the government about her is a more selfless act, it's about safety for her and the MC (and the world). No one knows if she's a pandemic waiting to happen or if she's in danger of dying from Earthen viruses, bacteria or whatever. While it's risky because there's no telling what the government will do, if it goes alright she has the government backing her and trying to help her return to her world because it's to their benefit (they gain a lot by studying her and her world if she succeeds).
Not telling the government is a more self-beneficial choice, you get your standard reverse-isekai series with fluff and waifu (
if she isn't a walking hazard). Great for the guy, not so much for the girl if she wants any hope of returning to her world.
@Memerk ET isn't remotely realistic, the government wouldn't want to antagonize aliens whom they don't know if they could retaliate for any actions we take or not.