Sounds like you had or are having a bad experience. Sorry.
Clubs won't fix any problems that you mentioned but could allow for more opportunities for more participation.
Advantages of public school systems: Allows for participation at a lot of different levels of interest for a limited period of time. Kids know they don't have to specialize and can still enjoy the activity that may have life long benifits. These systems aren't meant to be training grounds for the next level even though they can be for a small percentage of the total population that does attend. In my opinion, track and distance running has been making a comeback in performances in the last 10 years at the junior level and now at the pro level. It was a lot worse in the 80's & 90's. Another advantage is that little thing called money. It's not much and budgets are getting tighter but coaches are contracted, busses are fueled, entry fees are paid, schools are insured etc... to make the system that is in place work.
Disadvantages of a public system: As you mentioned, not every track coach is really a track coach or may not have the skills needed to teach all events well. Considering what the pay is compared to the hours needed to run a great program, it's getting harder these days to find people willing to commit to that kind of time not just for a year but for 30 years. Geographic location, population density, talent pool, climate etc... are always going to be limiting factors. Everybody deals with this to some degree. Those schools that have consistent high performing programs in all events are few and far between.
Advantages of clubs: Opportunity to focus on skill development in the warmer months of the year (summer)while not in school. Flexible schedules.
Disadvantages: Most important meets to most high school aged kids are during the spring. Not true with younger kids but they don't really understand what's going on anyway. Pull out the slip and slide and I know which activity they will gravitate toward. You better be willing to take on a lot of low skill/talent to be able to fund the things you want to do with your elite athletes that most club coaches only want to spend their time with anyway. Insurance, facilities, resources for running a program including equipment, implements, training room needs etc... are all going to have to be considered. Organization by a competent adult is just as important here. I've seen more lousy club coaches than high school coaches. Really developing a plan to help athletes grow and improve is not what I'm seeing most of the time. Most of the time, the club coaches I've observed don't appear to have an understanding of child development or a sense of motivating kids of all ages. They tend to look for prodigies and then try to do too much with them while they have them under their tutelage.
I'm looking at soccer, swimming, basketball, volleyball, orchestra, dance etc... clubs or groups that require money and parent support. How many talented kids never get these opportunities for the simple fact that they don't have the resources or parental support to participate. Public school provides an opportunity to explore and makes things available that otherwise wouldn't be.
I'm in agreement that there is a place for clubs but I think it comes in the summer months, after high school or college. Distance Running and Track & Field will never surpass the major sports in America in terms of popularity until the same money is available and that will never happen. Most of the rest of the world doesn't have the sport culture or money to support bb, bb, fb, etc... The best available Americans that are motivated enough to stick with it and excel will be who we can hope for. Not sure clubs will make all that much difference except to those that are just off of the elite but if they don't have the time to train at the elite level because they have to pay the bills somehow, I'm not sure you will find much more talent to develop anyway. There are clubs already in place like the Hanson group etc... for those distance runners on the edge of being elite.