This is very wise.
Some graduate programs allow you to see the list of students currently enrolled there, and also see where they got their bachelor’s degrees, or any other degree they might have already obtained. If you look at pretty much any of them, you will find students who got their bachelor’s degrees at a very wide range of universities. In most if not all very good graduate programs a small number of the universities where someone got a bachelor’s degree might be higher ranked than the schools on your list (such as Harvard or Stanford), but a very large number of students even at the very best private graduate programs will have come from schools that are ranked either about the same or lower than anything on your list. The students come from “all over the place” (this is an exact quote from a doctor I know, but it also applies to the students who I see for example in both daughter’s medical-related graduate programs). You are also likely to see quite a few students who went straight from a bachelor’s to a PhD, but also quite a few students who got a master’s degree along the way. Of course the master’s degrees will have represented an additional cost for the students or their parents.
I gather than you have not applied ED anywhere. I think that this is wise. I think that you will get a range of acceptances with a range of costs. This will allow you to see what actual offers you get and what each will cost you before you need to decide where to attend. Also, if you do visit a few schools with an affordable offer in hand, it will feel very real. You will know that you really can be there in September if you want. If you chat with a professor (which can be arranged at some schools) they too will know that you really can be there in September if you choose to do so.
From your list I do expect you to get a few rejections and a few very expensive full-pay acceptances. However, I also expect that you will get some very good acceptances to schools that will be relatively affordable (or at least way under the $100,000/year that the most expensive schools are getting close to these days).
Best wishes.