Yes, the amount of value-added from the mere name of your school is quite hard to measure and may be quite low.
I will say that I think colleges which regularly place a lot of grads in top law schools tend to have quite good advising, formal and informal, for the students with such ambitions, and indeed starting really even before you matriculate. Obviously that is replaceable with some effort and foresight. But much like with “feeder” high schools to the most selective colleges, making that sort of high-quality advising easily available is likely a significant part of the observed statistical relationships.
Like, a “trick” you will generally know about if you go to a T14 feeder college is to try to quickly identify a major and other courses where you will get really good grades. Again, this process can start before you even matriculate, and certainly has begun as soon as you start getting any evaluations in your classes.
And this is important because just banging your head against the wall in a major you thought you would like but is not really your best subject in college for a little too long can have permanent consequences for your college GPA, which is a critical input to T14 admissions decisions.
Combine this with the fact the T14 law schools do tend to go somewhat deeper into the classes at prominent T14 feeder colleges even controlling for test scores, and there is a much higher chance the people who know this “trick” will get the ultimate GPA they need at a T14 feeder. Whereas at a non-feeder college, the people at the very top of their class who do go to T14 law schools may essentially have all gotten “lucky” in that they were in one of the best subjects for them from the start, even without knowing this trick.
Now again, I just told everyone here the trick, and there is absolutely no reason you cannot apply the same trick at any college. But still, I think this sort of thing is the source of some of the differences we see, including determining who will be the 1-2 people at a top law school from a large non-feeder college and who will not.