I disagree with the idea that there's no logical point to Liz.
Unlike MJ and Gwen, she was in the comics when Peter was in high school.
And it allows Marvel/ Sony to go in a different direction, and do a film in which Spidey doesn't get the girl. Hell, he could realize that Liz isn't right for him, just as Aunt May introduces him to her friend Anna's niece at the end of the movie, allowing MJ to make her "You just hit the jackpot" intro.