I could name a number of facilities that show that AZA accreditation is not just for municipal zoos, including Disney's Animal Kingdom, all three Sea World parks, Dallas World Aquarium, The Wilds, and countless other facilities that are not municipally-owned (especially when it comes to aquariums).
As for changing the AZA, I for one think there are fair ways to improve the organization. For instance, more cooperation with the private sector would be a great way to have more successful SSPs (by private sector, I don't mean non-AZA zoos (although good ones should be able to cooperate too), I mean privately-owned collections/places that don't fit the criteria for accreditation). Shifting the focus of AZA accreditation more in the direction of animal welfare, and away from other matters would also be a positive change. While I do see the need for zoos to lose accreditation due to poor management (e.g. Columbus mis-management scandals, Lowry Park Zoo under Lex Salisbury), or other glaring problems, but it's truly a shame that there is a bigger precedent for accreditation loss due to finances than anything else. In reality, priority number one on the AZA's part should be animal welfare, and it's a shame when accreditation results don't reflect this. Some visitor-centric criteria also aren't needed- for instance I don't understand why the AZA should care about the pavement of pathways, while important for visitors, I highly doubt that the animal residents of a zoo care about the paths being paved.
I'd also argue the AZA would benefit from a greater influence over collection planning, especially in regards to similar species. Rather than having programs managed separately for Humboldt, Magellanic, and African Penguins, where the Africans are substantially more popular than the other two species, it would be of benefit for a change from individually-managed SSPs towards a "Spheniscus SSP", allowing space to be balanced more equitably between species. This would also be beneficial for other similar species- for instance with Gibbons (this one is sort-of already one SSP, or managed that way, however with more guidance over which species are being held, I'm confident the AZA would be able to manage a fourth gibbon species as well), some ungulate programs (e.g. incorporating Nyala, Lesser Kudu, Greater Kudu, etc. into a "Spiral-Horned Antelope" SSP), Callicthrids (to compensate for the over-popularity of golden lion and cotton top tamarins), and any other place in which there are multiple similar species that could benefit from re-allocation of holdings. While it may be a slippery slope, I also wished that the AZA would do more to enforce involvement in SSPs, and either encouraging or pressuring zoos to choose a threatened, SSP species instead of a common, unmanaged species (best example for this would be re-allocating waterfowl holdings away from White-faced Whistling Ducks, Mandarin Ducks, and Ringed Teals- three common species with no conservation value). While I can see the argument made for deference to zoos in regard to collection planning, it would be nice to see the initiative taken- either at the AZA level or the institutional level- to level the playing field and create more of a focus on species of conservation and educational importance.