If anything, the predominant messaging today is the exact opposite of that. It also doesn't matter because public loans qualify for income based repayment, so it doesn't matter. If you end up stuck working at McDonalds for the rest of your life, you'll never pay back a dime.
>60k, with an extremely high interest is most definitely a problem.
Current undergrad rates are fixed at 3.73%.
>Anecdotally, my group of friends all flip between "school name"/School/Uni in conversation.
Interesting, (as an American myself) I've never heard an American use uni outside of conversation with Europeans.