Here's my take (and this is somewhat timely, because I went for my first run in a year this AM):
I used to run exclusively. I was, in hindsight, not very strong outside of the ability to drag my carcass long distances. I found strength training, it fit better with my goals and my schedule, and running fell by the wayside.
I ran for 20 minutes this morning, and even after a year of S&S and RoP, I felt like I'd been through a steamroller when I was finished. But I also felt really good mentally; I had to negotiate with myself for some of the long slow uphills, and it took a lot of willpower not to walk. I am very glad I ran, and my current goal is very modest-6 miles per week (2miles 3x a week), working up to around 12 miles per week (4 miles 3x a week or 3 miles 4x a week). I'm not running to train for 1/2 marathons anymore, I'm just aiming to run because there's something really relaxing and mentally freeing about a 1/2 hr to 45 minutes where the only thing that matters is relentlessly moving forwards. Outside, in rain or shine, getting air and experiencing the seasons and the world changing each run. Will it improve my endurance, and probably round out my workouts slightly? Absolutely. Is that why I'm doing it? Nope. I've hit a point in life where running isn't my primary exercise, this is purely for the experience.
Now, having said that, as far as exercise and fitness go, I have found that strength comes more naturally to me than running. At best, I might get my mile times down to 10 minute miles at a relatively easy pace. But I know I can clean and press a 25lb kettlebell over 50x, I can swing a 50lb kettlebell 100x in 5 minutes, I am learning to snatch...and I feel my body responding and changing positively in a way that it never did from running. I never felt like I had massive improvements in running beyond endurance-I never picked up speed naturally, and it took me a brutally long time to break 30 minutes in a 5k. But I've experienced progression in kettlebells, and I find a different kind of fitness and peace there.
But I don't think you can discount or dismiss the importance of spending time outside exerting yourself to move forwards. Whether it's a walk, a run, or a hike, there's something mentally soothing you can't capture in any other way.
(As an aside, treadmills can burn in hell. I've done laps in parking garages over running on hotel treadmills. I regret nothing.)