K. I've been thinking about this. I feel like there is an advantage to going to a more competitive school. Not sure I want to incentivize the cheapest school. Would be interested in others feelings on this.
I went to a small private tech school, not widely known, and I chose it largely because they offered me a full-tuition scholarship. My other alternative was the state flagship, where I just so happened to end up going for grad school. In retrospect, knowing what I know today, I would have chosen the small school even if they were the same price; if money was not (as big) an issue, I would have gone to the smaller school even if it was slightly more expensive. I liked the small classes from day 1. I liked the number of project and lab classes in the curriculum. I liked the kind of people it seemed to attract (I got to live on campus for a weekend when I interviewed for my scholarship and meet many of the students). It was easier, for me, to find a niche on that campus; I expect I would have gotten lost at the state school, but as it was I got to tutor and research and even TA as an undergrad and lead some student groups. I liked that the school was in the city and not a cornfield, so there was much more to do on the weekend than get drunk and hook up (though those who were after this did find opportunities). And while, nominally, it was less competitive, the classes had plenty of academic rigor; having TA'd a senior year lab course at the state school, I can say with certainty the students were no better educated than my classmates and I from the small school. The state school is in the top-10 for engineering...there's just not that much difference in academics, at least until you get to the very elite level schools (I know a few people who went through MIT, and they have a lot more depth to all their coursework).
I partly agree with you; depending on the degree of "more competitive" and "more expensive" it might be worth it. But one important thing to note is that college has a significant "you get out what you put in" component. A student that's not particularly driven to seize upon additional opportunities won't get a significant benefit from a marginally more competitive school in terms of education. Only, perhaps, better job fairs and entry-level employment prospects due to name and alumni recognition. But a motivated student will create those opportunities for themselves even at a less recognizable school. All the graduates of my cohort and the years on either side are gainfully employed using their degree, or pursuing/nearing completion of graduate work (some have finished masters and are now working).
I think what ends up being more important, as far as education rather than reputation, is not how competitive or selective a school is but some of the details people forget to consider. What classes are in the curriculum? How many are hands on, project based, laboratory courses, or otherwise emulate the real world (whatever that looks like for non-science/engineering/CS)? What resources are available for students to pursue extracurricular projects? Is there a "fab-lab" or shop, site licenses for key software, IP/entrepreneurship office? What kind of student groups are active (robotics, student consulting group, school newspaper, volunteering, etc)? How good is the career center (at educating and catering to [desired major])? I didn't know to ask some of these going in, and I'm sure there are many more. But these sorts of considerations give you insight into what people *do* on campus, and at the end of the day, doing is the best way to learn and being surrounded by people doing things (besides going to lectures) is a great way to be motivated to do them oneself!
I think it might be hard for you to put the right incentive into the contract because Kid 1 might be super-motivated and academically inclined whereas Kid 2 might be smart but disinclined toward academic structure so they'd get all they need/want academically from a lower-tier state school (e.g. CSU vs UC system for CA). But it probably wouldn't look fair to them if you said "Kid 1, have $5k extra to go to Prestige School because you'll benefit from it, but Kid2, you should go to a cheaper school." So maybe you just leave it open to reasonable negotation. So Kid 1 comes to you and says "look, I got into Prestige University and I got these scholarships but I'm still $5k short but PU has all these benefits:" you can say, "ok, you've convinced me, that sounds reasonable" (or "ok but this is a loan" or whatever you want) and when Kid 2 comes to you and says "parent, I can clearly see I am saving you $10k by going to Community College and then Cheap College, and I know you gave Kid 1 $5k to go to PU, why don't we split the savings" you can be like "that sounds fair, yes" I just don't see a way to "lock it down" in your contract and still motivate your kids to make good decisions...