Since David was a politician, couldn't Elise have just looked him up?

As she said, when he didn't call her she assumed there was a reason for it. She moved on.

Of course, she could have reached out any time....she did the wait for him to contact her thing and if he doesn't that means he doesn't have interest.

That is the most realistic part of the entire film. Most women are like that...wait for the men to pursue, initiate contact, ask out on the date, decide what to do on the date. Most women do not pursue men.