I personally would not allow my child to do this too many things can happen. I am a airline pilot and with the load factors today and reduced turn times for connecting flights too many things can happen leaving a minor stranded. Even if the flight is direct you can have to divert for weather or maintenance. I do not think a minor can rent a hotel room and in some locations the 3rd party gate service personnel escort the child from gate to gate. Many people do it and think a FA is dedicated to their child and that simply is not the case.