Sedentary sharks are commonly and easily kept in home aquaria, as long as their specific needs are met.
A 600+ gallon tank is well above the recommended volume for cat, epaulette, and bamboo sharks.
Instances of angels picking on sharks can happen, but is much, much less likely in larger tanks. The OP's tank is substantially large enough to, in general avoid this, though there are always exceptions.
I would also contend that in many cases home aquarists are far better suited to provide for the needs of the fish in their care.
First, home aquarists are much more emotionally invested in their fish, than that of an underpaid staffer at a public aquarium. It is not a job to the aquarist.
Second, the hobbyist is more often tuned in to the relatively few fish they care for versus the large amount of fish at a public aquarium.
Thirdly, the home aquarist spent his own hard earned money on his livestock versus the public aquarium that has public or other funds to use.
Home aquarists are also able to utilize veterinary services as well.
Things can and do go wrong in public and home aquaria. There are many instances of following compatibility rules with fish that should work together, but don't. There are certain risks inherent in keeping any 2 living creatures together, but basing it off of the majority of the experiences of others is the best way of doing it. And while there are some instances of picking on sharks, in an appropriately sized tanks this is not the majority of the instances.
Holding on to outdated aquarium dogma is up to each and every person, but in my recent experience, and that of others is that the OP's stocklist will not present an issue.