I agree with @MySonsPlay. Being exposed to different coaches through the career is better (IMO) than staying with a single coach for a long time. My kids have learned something from every coach they've had, even the "bad" ones. If a coach goes to a nearby club and you're happy with the coach, sure that should factor in, but shouldn't be the only factor. YMMV. Granted, if you get a coach you don't like, maybe a different club is the correct choice.
I tend to agree with @justanothersoccerdad over @MySonsPlay though I think both have valid points. But, what exactly are you paying for? High quality instruction I think is a main component of the reason to join a club. That said, I recognize that there are various styles of coaching, and I would be fine under varying styles. It also depends on the cost; some clubs cost more than others, and I think the more you pay the higher quality the instruction should be. The higher the fees, the more experience and higher licenses the coaches should have; after all they are getting paid. If they are volunteer coaches then the fees should be low and sure, you should not have as high expectations. Perhaps it's a moot point as even the coaches we have come up against I think are fine coaches. Haven't seen any bad ones yet, but I'm sure they're out there.
You pay for: * Better Coaching (presumably, but not always) * Better competition (the leagues & tournaments clubs attend) * Better Teammates (again, presumably) * Better Facilities (presumably) You might think that, but I think it's far from a rule. US Soccer has different "licenses" of coaching (https://www.ussoccer.com/coaching). You don't have to have a license to coach, but it's an indication that a coach has had certain training/experience. "Professional" is the highest, but for youth, A is the top, then B, C, and D. We've been in a small club and a large club (ie: expensive). The large club didn't always mean the coach had a higher license. I think most club coaches are NOT volunteer.
"Presumably" is exactly right. From my p.o.v., many parents just assume that the clubs deliver precisely what the marketing literature specifies; that's simply not true. Where coaching licenses are concerned, the same thing happens: "Oh, wow, Coach so-and-so has an A license! I want my kid on his team." I have encountered several D-level coaches (and below) who could wipe the floor with A-level types. As with any investment, always do your own due diligence and always have an entry/exit strategy. Even better---teach your kids how to size up these sorts of things.
Different is definitely a good thing...up to a point. You're looking for coaches who can help your player grow. If a coach can't help your player to grow, don't even bother---everything else is just noise. And players need to develop a sixth sense about which coaches can help them grow, as it's not always obvious to parents, siblings, etc. E.g.---My daughter privately trains with a coach who's not always considered to be a "good" coach by some of the local, self-styled soccerati types. He's got some rough edges, to be sure, and he only trains who he wants to train (mostly boys), but he's a hell of a good coach for the right types of players. Well, she picked him out (and he agreed to train her, mainly because of her relentless focus) because she knew that his approach was exactly what her game needed this year. Indeed, it was a great choice on her part. She also has an excellent club-team coach (with a much different, more cerebral style than her private trainer) this season, so she's situated herself in a tremendous place. I suppose that what I'm getting at here is that if a player sticks with a coach over several seasons because that particular coach continues to bring out new facets of said player's game, what's not to like? I have found that good coaches will also let players know---sometimes subtly---when they need to seek out someone new.
There some clubs... though not sure if "club" is the right word... but they market themselves as an affordable alternative to the expensive clubs. They are somewhere in between rec and club. They generally run about 1/4 the cost of a comp club and they take more breaks so the kids can do other sports. The coaches there are volunteer; that's partly how they keep the costs down. They do play in tournaments with clubs and sometimes seem to hold their own. But yeah not sure what you call them, maybe a select team? And maybe not every city has this.