Read carefully:

Annabeth never kissed Jason on St Helens

Athena wants Annabeth and Jason to get together

Jason's and Annabeth's relationship is kind of forced. There is not much feeling.

They are basically best friends with benefits

Jason didn't get a choice for immortality; he was given the choice to choose his own weapon. Here, he got his coin- sword/spear, as well as a blessing from all Olympians.