When you say state schools, UCs and highly competitive privates - what is your state?
The UCs OOS won’t give you money. UCLA is over $70k a year now. Michigan the same. But with a 4.0, U of Arizona, for example, would be $25k ish a year OOS. Bama $20k. In most areas (not sure what is being studied), do you really think there’s that much a difference to a UC? Or schools like Florida, South Carolina, UGA are much lower cost relative to UCs - and while we don’t know her overall profile, kids with a 4.0 and 1530 are a dime a dozen at all these schools.
Top privates will have income scales and know that your assets will be a part of it. When I spoke to Cornell, they told me a million in assets, regardless of income, will likely leave you with no aid most anywhere.
Your home equity and other assets might be included, depending on the school. My daughter got into a school where 88%of kids got $38k on average. It was an income based scale. We got none. I asked why. They said because you had more than normal assets. I asked what’s that ? They said 2x income - which isn’t much.
So if you want highly rejective - go for it. Run the NPCs first. No point in applying to a need based only school if you can’t afford the # it spits out.
But there are many smaller, strong privates that do give merit. Some half or more. No, they’re not Ivy or NESAC. But schools like Depauw, Kalamazoo, etc are strong. And you have the Johnson at W&L, Presidential at American, and full rides at schools like Vandy, WUSTL, Emory, Miami etc
If you’ve ensured an affordable safety then why not ? But @twogirls noted budget has to be determined up front and made very clear.
You only apply to schools that can achieve that #. They may not but can. And ensure two that will and that are assured admits where the student would be happy to attend.
And if cost matters and you want pedigree, apply widely. You have 20 common app spots - use them - but note it’s a ton of work and many students wear down early in the process. It’s essays galore.
Good luck.