I have to disagree. For the exact reason that you state, that people who stop have a reason to do so. I have only found over the years that people who stop to give rides to hitchhikers are people who have hitchhiked themselves, or are people who are looking out for your best interests, i.e. people who think that by picking you up they are "saving" you from other people who might have a less than altruistic plan in mind.
As a hitchhiker I have never had problems with people who have offered me rides. Instead I have had problems with people in towns. People who do not travel and have never had to ask strangers for help.
As a 5'2" female, I have safely (with the exception of a skeezy trucker that realized I was a fighter) hitchiked from Illinois to California and all around the West alone. I had difficulties going further South than Memphis and have been stuck in Indiana so many times that I choose to drive East. I have met many a family with a benevolently concerned parent, interesting single older men and women that wanted company on long drives, and those who hitchhike themselves. Hitching has made for great experiences, friendships and a return to the trust in humanity many have lost. Congrats on the fantastic post about a lost mode of transportation!
Truly,
H