There is not one and only one, right answer to the question of which way to go. Dive clubs can be VERY SUCCESSFULLY affiliated with stores, and not lose their ability to serve as a general meeting point for divers, or a source of socialization, or an educational forum. Dive clubs can VERY SUCCESSFULLY operate independently of any particular store. A lot depends on what you you want the club to do.
My experience is that a driving force in the success of any dive club is the passion of the leadership (not necessarily the members). And, too often the passion of the individual who starts the organization is not sustained over time by others, even if those ‘others’ voluntarily accept a leadership role. That can be true whether the club is shop-affiliated or not.
My experience in two states is also that dive clubs NOT affiliated with / supported by a shop generally have a harder time sustaining activity over an extended period of time. They come and they go. They go through periods of vibrant activity, and they cease to exist, after which they are resurrected, and go through periods of vibrant activity, after which they become dormant again. That is a general observation, and there are notable exceptions.
We have several dive clubs in our area, both ‘informal’ and ‘formal’. The informal ‘club’ – now about 2 years old - is really a Facebook-based entity that has a standing weekday evening dive time at the local quarry, attended by ~2-20 divers, depending on the season, and the vagaries of individual schedules. The Facebook page provides a site where divers can link up to dive locally at other times, to be made aware of charters, training opportunities (e.g. shop classes, or activities set up by individual members or a group of members), used gear for sale, etc. The affiliation of participants crosses shop lines. At times (during summer months) some people may bring food / beverages to enjoy after a dive, but that is an individual decision, not a club-sponsored activity. There are no formal meetings or speakers, there are no officers, no dues, etc. It works well. It was started by a couple of divers who work in the IT industry, and one of them in particular is responsible for maintaining (and policing) the Facebook page. Were he / they to move away, or lose interest / enthusiasm, it might or might not continue. But, it is a minimalist club.
The most successful ‘formal’ club in the area is one that is store-affiliated – the shop takes responsibility for planning (and running) monthly meetings at a local restuarant, arranging for speakers, setting up monthly cookouts May-Oct each year, and hosting a great Holiday banquet each December (frequently attended by staff / divers affiliated with other shops in the area). But, the key ingredient is not necessarily that it is shop-affiliated, rather it is the energy and personality of the owner of the particular shop. The speakers he schedules are excellent – they are both local and regional - the meetings are a great opportunity for socializing over food and drink (usual attendance is 25-40 people, and the Holiday Banquet has sold out every year for the past 5 years (100 seats, $50 / person). I believe that the shop-affiliation contributes positively to the number of divers who regularly participate. Yes, it is clearly a shop-affiliated club. But, it is open to everyone, and divers / staff who are linked to other shops do not feel uncomfortable participating – it is not a partisan organization. BUT, it does NOT EVER meet at the store. That would create an more uncomfortable situation and probably undermine the vitality of the club.
The point is, you can go either way (shop-affiliated or not) and be successful. The key is having an individual;, or small groups of individuals committed to maintaining it. Dive clubs are generally not self-sustaining. Again, there are exceptions to every rule, but that is a general fact.