My stories:
My first two years of high school, I didn't keep a running log. I estimate that I ran between 30-40 a week freshman year (never ran seriously before high school) and maybe a bit more soph year. I ran 4:37/9:54 by the end of freshman year. Soph year, I got down to 4:30 but barely improved for 3200 (9:51). I was frustrated with what I saw as stagnation so I started keeping a log during my junior year. Started in the winter, I had built up to a consistent 60 mpw avg with workouts. That year I crushed my PR in the 3200 down to 9:24.
In college, a similar pattern repeated. I had run 70-80 mpw during my freshman year. In the winter of my soph year, I read into SOM on the letsrun boards and got inspired to start doubling as much as possible. I got up to 100 mpw doubling every day. My 5000 pr that year was 14:46.
The next summer (soph-junior), I took mileage seriously. In hindsight, too seriously. I set myself the goal of getting up to 120/week avg by the end of the summer. I didn't get there, but averaged above 110 for probably 10 weeks. I ran much better in XC than I ever had, but I think looking back that if I had run a bit less mileage, maybe 10-15 less per week, I would have been able to run stronger workouts, not been so tired all the time, and perhaps run better.
That spring, I got my 5000 PR down to 14:22.
The next year, my 4th year, our men's NCAA teams got cut so I had the freedom to train for whatever I wanted. I ran a half marathon in the fall (1:07s) and trained for track in the winter/spring. Those seasons, I kept mileage high but was more used to it and able to perform better in workouts. I focused more on the 1500/mile than in previous years so mileage dropped a bit when specifically training for those. I surprised myself with big PRs, running 4:08 indoors and 3:49 outdoors, while doing 90+ a week in the real training blocks and workouts geared towards the 5k.
TL;DR - Higher mileage WILL yield benefits, but like everything else there is a point at which you hit diminishing returns and you need to emphasize other aspects of training. Don't run mileage at the expense of everything else, but recognize that it is an important support system for all of your faster running.