I think most titles should be reserved for professional environments. I think it's weird to call people by their titles outside of a professional situation. Like, my husband is a Lieutenant Colonel in the military. He ONLY uses that title at work. No one outside of the military ever refers to him as "Colonel." He is Mr. T.
Similarly, I feel like PhDs should go by Mr or Mrs or Ms rather than "Doctor" in general interactions. They can be referred to as Doctor in academic or professional situations.
Now, medical doctors are a little different, IMO. Since they are basically always "on duty" in terms of their ability to be helpful in a medical emergency situation, I feel like calling them "Doctor" outside of work is useful and conveys their status as a potential helper.
I know this post is in response to "Dr. Jill." My opinion on this one is that if she is speaking with authority on the subject where she holds her degree, absolutely refer to her as Doctor. Otherwise, probably not necessary. Although, as First Lady (elect), she does have a bit more riding on people knowing her qualifications, especially if she plans to use her position to push an educational initiative as her pet project.