Fitness & Nutrition has been up for almost month now and running has 36 questions out of 309 in total. After the rather generic exercise tag, it's by far the largest tag on the site.
I personally find statements like:
you would get a lot of amateur answers to questions that require more experience
I probably wouldn't bother with a more general site
to be very much against the spirit of Stack Exchange. If you're an expert: prove it! The votes will show everyone who gives the best answers. Furthermore, we try to enforce 'Back-it-up!' on answers, which should help to prevent amateurs from answering without preparation.
A lot of our users don't perform just one type of exercise. They might be doing weightlifting or martial arts, but they also run or do some cardio. Just as lot of people on a diet take up jogging as their main source of exercise to lose weight. There's so much cohesion between types of exercises and related topics that I don't see why they have to be separated.
The only thing that counts is that runners get great answers to their questions and that the running-experts have questions to answer. So simply put, the site you're looking for already exists and there's no reason not to start asking questions!