Makes sense
Certainly get a financial safety, but if you can swing the in-state cost of Michigan, I think the chance to excel in a competitive school and do research for one or more rock star faculty members definitely swings in favor of Michigan.
PhD admissions are made by the faculty themselves. When you apply to grad schools, you have to write a statement of purpose and discuss the research of several professors in the departments with an eye to what you might do. The most important factor is your letters of recommendations. Professors don’t want a lot of risk and the ones in the top schools don’t have to take a lot of risk. Getting recommendations from people who themselves are highly respected carries a lot of weight.
It’s not unheard of for graduates of schools like Alabama to get into top programs, but doing well at Alabama and doing well at Michigan don’t send the same message that you’re a rising rock star yourself.