Exactly. That’s why I tend to recommend CTCL schools, especially for a good combo of financial & academic safety – frequently they do a great job meeting need. They don’t guarantee to meet 100% of need, but if they want you badly enough they can put together terrific packages.
Obviously your mileage may vary, but our experience was great, and we met a TON of people at honors events who were shocked and thrilled by their FA packages. I imagine this is much less true when it’s not a safety.