Well ... I can't speak for departments in general or specific states in particular, but I did just come back from the Green Mountain Iron Dog, which is a competition in Vermont that is for both police K-9 teams and civilians, with several of the competitive events being law enforcement only (such as the drug search and building search) and several being shared.
So, based on the folks I've met there - more law enforcement teams than civilians - and interacting with them, talking with them, etc. here's my opinion.
First, choking a dog off the bite is not the norm among law enforcement agencies. It is not with the military and it is not with the (mostly Vermont) K-9s I met at the event. Actually, one of the required tasks in the building search is to CALL the dog off the bite AND back to the handler, no physical contact allowed. (The officer remains at the threshold throughout the search and gives no commands to his dog except to call him off the suspect and back to him.) As most dogs ran 17 and 18 second times in the building search between entering and returning to the handler after getting a bite, it stands to reason that they had no issues getting their dogs to "out" on command and therefore have no need to choke their dogs off to get compliance.
All but one of the handlers I talked to at the event take their dogs home where they are a part of their family. Their kids play with the dogs - several of their kids and spouses were at the event, too, playing with the dog, petting the dog, holding the dog. These dogs go home after their shift and interact with the family, they don't go back to the kennel. (Military working dogs, on the other hand, go back to the kennel, not home with their handlers.)
As far as "obvious reasons" why civilians may not be allowed to observe normal training would be the liability factor. What happens if you position yourself where you shouldn't be and the dog bites you, for example? That seems to be the most obvious reason I can think of.
Then, of course, there would also be a concern about screening people to ensure that they don't show all their training secrets to crooks who would use them to "reverse engineer" the dog's training. When civilians request to do a ride-along with a local law enforcement officer, they generally have to do paperwork, get fingerprinted, and pass a background check before they're allowed - they don't just get to ride along. Again, it should be obvious WHY. I would assume that something similar could be done for someone wanting to observe K-9 teams but such a program, unlike ride-along programs, are not generally in place in most areas.
Just some thoughts.