There are iirc 66 universities in the US that offer to meet the full demonstrated need of all students admitted. Not all of these are no loans schools.
There are 115 (iirc) schools with need blind admissions.
There are 12 schools that offer to meet full demonstrated need plus no loans policies.
There is a good deal of overlap among these categories.
The crux is 'demonstrated need' but this is very clear-cut in many cases, and students holding more than one offer can haggle.
There is also a tier of universities offering various packages to meet a portion of the cost of attendance but not 100%.
Cost of attendance means room and board, tuition, books, general fees/ university sponsored health insurance, and travel costs.
In general, if your family income is less than $150k per year you will be offered some financial aid (aka a portion knocked off the total cost of attendance). Many private universities make allowances for proven estrangement from the main breadwinner in cases of divorce / abandonment when normally both parents have to fill out financial statements. State schools in general just ask for the financial statement of just one parent if divorced/ abandoned or if an untraceable / estranged parent is part of the picture.
State schools tend to be cheaper than private schools on paper, but when you factor in the financial aid offered by many private schools you can end up doing better in a private school. Not always, but often.
Student loan problems are certainly a big issue. Some students don't get the sort of jobs upon graduation that would enable them to easily pay back loans. Some students choose courses that don't lead to improved chances of graduate-salary employment. Some choose colleges whose reputations are not great. Some students should have chosen a path to a degree that involved two years in a community college followed by a transfer to a four-year university. Some students should consider taking a year or two out of school along the way to their degree to work and save and build their resumes instead of trying to get it done in four straight years and get the college experience under their belts. Some students should do whatever it takes to graduate and not drop out while still owing repayments. There are many factors behind the student loan issue. I'm fully behind Biden's efforts to write off loans, because large loans dampen the economy.
If a child of mine needed to take out $100k to get a degree from any university in the top 20, I'd encourage them to go for it, but to make sure they studied economics, finance, or engineering, or something else that would lead to an excellent salary by age 30. There are people who take out loans of that size to do communications at small, obscure colleges.