The best coach my kid ever had was with a small local club. The problem, as you note, is that unless you get a group of really good players that become friends and are capable of lifting the team to a new level (and there are plenty of examples where this does happen, but it has to happen early on in the process), you'll have the promotion/relegation issue. The team won't advance. After a season or two the best players become frustrated (particularly with the weaker or less dedicated players that aren't putting in the time)...will be ready for more challenges....will leave....you'll have to recruit new players. What's worse, in the younger ages they are probably playing in the key positions down the center line of striker/CM/CB/GK. so their departure is a particular blow. The middle tier has now been playing for 2 years and is ready to move on, but you have to bring in new players up from AYSO to fill in the gaps of the players that left and it takes them a season or two to get up to speed so that middle tier now wants to move on....rinse and repeat and you find yourself perpetually stuck in bronze. Works the same even without pro/rel since if you move too fast your team will be kicked 12-0 and the parents will complain and go elsewhere. If you are lucky enough to actually achieve promotion, that first year in the new tier is a bear because all your players are adjusting to the new level of play and you are playing teams that survived that level of play last year...you not only have to avoid relegation, but you got to be good enough to hit the middle of the table. That's why many coaches will upgrade using the promoted level to recruit better players instead of developing the ones that brought you to promotion.
It's a perpetual cycle for the smaller clubs. The only thing that really holds some of them in place is the field space access, particularly in the suburb towns, since school districts and parks and recs tend to give preference to the smaller local orgs. My son played for a heavily latino team that practiced in the public park....bear of a time recruiting any nonLatino players....every single anglo player that showed up looked at the park situation and said no thanks.
The other big factor is Coast v. SoCal League. Not a whole lot of local clubs in SoCal League, unless they've somehow affiliated themselves with some other club as a franchise. In Coast, if you get promotion early enough, you can get teams from small clubs that thrive. A lot of those Coast teams are heavily ethnic too from local barrios and not just Latino. And AYSO United has become a recruiting machine (being able to get first dibs on players coming out of Extras or Core) and plays in Coast, but increasingly, I think their membership in Coast is going to hold them back if they don't make the hop to SoCal League.