Where you graduate from (or where you are an alumni of) is part of your prestige. If you are a newly minted PhD you don’t have any breakthroughs in the field. So search committees are looking for assistant professors with the potential to make breakthroughs in the field. And many times they determine that by what school you graduated from and who you worked with.
It doesn’t “just so happen” that people doing great research graduated from top schools (and also work at top schools). Top schools attract a lot of things that make it much more likely that you will make breakthroughs in a field. For example, when you submit a grant to the NSF or NIH, there’s a portion of the grant called “environment.” They rate how well they think you will be able to achieve the goals of the grant given your institution and the support there. Top schools get much better ratings in this area than other schools, which raises the overall ratings of your grant. You also get higher scores if you work with more well-known scholars (who are usually at top schools). And top schools have the grants infrastructure to refine your grant and work out an acceptable budget, subcontract, etc., whatever you need. You need the money to do the work.
That’s one of the reasons top schools attract top professors, the ones making the breakthroughs in the field, who can be your mentors and bring you into big research projects that get you papers. They also are flush with money, so they can poach those professors from other schools.
So no, faculty graduate institutions are not usually a mixed bag. Go to the departmental website of any top department in a field and see where their faculty graduated from; I guarantee it clusters near the top of the rankings, perhaps with the exception of one or two faculty members. I did this exercise for the MIT EE/CS department one time for someone else and found that out of that enormous department, the vast majority of the MIT EE/CS professors graduated from just three departments: MIT, Stanford and Berkeley. There is the occasional appearance from UIUC and a few other scattered top programs.