Even if the student at the high school has some other safety? E.g. maybe the student has a 3.8 GPA and a 33 ACT, and his/her two favorite schools are the University of Alabama (automatic full tuition scholarship) and Tuskegee University (automatic full ride scholarship).
We also strongly advise every student to apply to CUNY in order to have a financial safety. Parents and students change their mind; just like the examples on CC, some parents give their kids no financial parameters, until the award letter comes in and then they tell the student what they will or will not pay. You also have parents who veto a school as being too far, don’t want to pay for flights, etc.
As far as the CUNY process is concerned, if a student was shut out (and can and do get shut out, especially at popular programs and at schools that have adopted a more holistic approach; essays recommendation letters) the default used to be admission in the community college in your home borough. Now what CUNY does is send you a letter asking that you add an additional 4 year school and an additional community college). We send reminder letters home letting parents know that their child did not apply to CUNY, in addition we, i-log the process (yes, parents do complain to their district/network offices if they feel their child has an unaffordable option, so at my school we cover all of our bases).
BTW, we ask for students to submit the the school where their final transcript should go on May 15. We then confirm the school again on the last day of school, when they sign for their diploma. We also send letters home about this. Since guidance and administration works two days past the last day of school, we discharge students then send out the final transcript. We let students and parents know that there will be no transcripts sent over the summer and they could be at risk of not being able to register in the fall (as our building is closed until the last week in august and most schools will not take an electronic version of the final transcript, working summer school is held at another site).