Now your replies seem more contradicting and redundant than they are a question. If you teach your dog everyday, that means your dog has the capacity in his mind to learn something new everyday. Therefore, if your dog learns something new everyday, that makes him susceptible to be curious of much broader things. And, like you said.. since you teach him new things everyday than would training him ever end? The common sense answer would be no, it wouldn't end if you taught him something new
everyday.
Just like the cliche phrase "Curiousity kills a cat", I'm sure it can be applied to dogs.
I crate my dog because I don't want him to harm himself in anyway. And the reason why I crate him is because, yes, I am presumptuous of what he might do to himself. I know that he is curious by nature. He loves to sniff. He'll bite anything for the sake of biting and taste something for the sake of eating. I am not there to watch over him, that is the difference of letting him out when I am home and putting him in his crate when I am not. I feel much more safe knowing what he's doing, what he's chewing on and playing with and if he is anywhere in harm's way. It seems like you aren't considering the fact that dogs learn new things on their own everyday, on top of things you may train them. My point is, when I am gone and noone is watching I don't want him getting into something he's not supposed to be getting into.
but what about when you are home? does your dog do those bad things that you are afraid he will do when you are not home? No, because I am there to watch him to make sure he doesn't get himself into those predicaments.
As for the dog park, you are watching over him are you not? That's a different story. The majority of crating and what people have explained to you is that we all crate them when we leave the house and noone is watching. Comparatively, it would be you leaving your dog at the dog park and leaving him there for two hours and then coming back. Wouldn't you wonder and worry about what he did for those two hours or if anything happened?
It's not really a trust issue, it's a I-Worry-My-Dog-Is-In-Trouble-When-I'm-Gone issue.
And no, I'm not justifying my crating with the fact that my dog is not allowed in public places. But he wouldn't be crated if he were.