Because it's a dumb, not very good science fiction film whose writers probably weren't thinking that far ahead in terms of the plot.
The ending was for him to give her the gift of a baby. The ramifications of her spending time with an Alien were probably not very high on the scripwriters priorities.
Dumb film for dumb people.
Was it a millionaire who said "Imagine no possessions"?

Because its Hollywood- a movie. The ending sort of leaves you to think that yes- she would be confined and interrogated to some extentnever mentioning the sexual encounter on the train or her pregnancy, then left alone and forgotten by the feds.as she goes on with her life and 9 months later has the baby while maintaining a low profile. Keep in mind this was the 1980's- somewhat easier to slip into obscurity than now.

Good question! I asked my mom the same thing when I was watching it with her last week. Since she had contact with the alien for 3 days, spent all that time getting to know him and knowing more about his being, the government would have grilled her to get anything out of her. Plus, they would have done tests on her like they did with poor Elliot in E.T. And since she was pregnant, they would have probably kept her or done tests on the baby after it was born. Luckily Starman said the baby will be human.
But I had the same question you did. Lol
All we have to decide is what to do with the time that is given to us. -Gandalf the Grey

Maybe they left that for the sequel, and then forgot to make it.
Ooooh, you wicked, wicked monkey! Robin Williams in Mrs. Doubtfire