It might be lower than that at a few rich, super selective schools … if you can get accepted.
https://www.usnews.com/education/best-colleges/paying-for-college/articles/2016-09-19/colleges-that-claim-to-meet-full-financial-need
For Stanford, I get an estimated net price of $9800/year (assuming $100K family adjusted gross income, $10K in checking, $50K in home equity, 2 siblings, and no student assets). The estimated parent contribution is $4800/year; the estimated student loan is $0. However, student loans could be used to offset all or part of that $4800 parent contribution (which is below the federal student loan annual limit).
Now, that’s Stanford, so good luck with that. In determining your EFC, nearly any other college is likely to expect at least as large a parent contribution as Stanford does (and possibly more than you could offset with student loans). Unless we’re missing key information about your situation, then realistically, you probably can’t count on such generous need based aid. So yes, you may need to focus on merit scholarships available from less selective schools.
Do run the online net price calculators for various schools that interest you, then discuss results with your family. If you have specific estimates for specific colleges, maybe your parents will open up a bit more.