I think you take the Naval academy out of the decision process because it is so different. She either wants it go or doesn’t, and cost is NOT the deciding factor. You would not decide between UVA and Naval academy, but USNA or not USNA. (BTW, my daughter did consider the USNA and USCGA, but decided not to go that way)
I don’t agree that the cost of room and board is the same at every school. I have two freshmen this year and one’s cost is about $7500, the other’s is $13500! The more expensive one could have been lowered to about $12000, but then she wouldn’t have been able to be with all the other freshmen (about 80% of freshmen live in the ‘freshmen village’ and that’s more expensive). $5000 here, $4000 there, and pretty soon we’re talking real money! Another decision she’d have to make at Bama is sorority or no sorority, and that’s a big, expensive decision.
To answer your original question, I’d strongly point my kids to ‘free’ but if I could otherwise afford it, I’d let them make the decision if it is within the budget. Most of us could have sent our kids to much cheaper options like community college or the military, but didn’t because money is not the only factor. We decided what the budget was and many kids left a lot of merit money on the table at schools that weren’t what the kids were looking for.