It depends on the context.
In a card routine, like we've been discussing, it's advantageous to let the audience see that the deck is normal. Then you should be able to several tricks with it, including letting the specatators handle the deck at some point. What happens is a cumulative effect, especially with people who've never seen you work before. As you do more and different card effects, it begins to dawn on them that you are responsible for what's happening, not some "trick deck." This is true no matter where you do magic, or under what circumstances. People think that almost everything a magician does is via gimmicked props, since stage illusions work that way and we've all seen cheap plastic tricks. It's a constant challenge you deal with professionally, because most people have never seen sleight-of-hand magic live at all.
Once they're convinced you're using normal cards, you then have to learn to perform sleights so they're undetected as part of the trick. That takes years, but is very very gratifying.
When you can combine sleights with an occasional gaff, you take the audience unaware. That's a lot of fun, although you can only share that level of it with your fellow magicians.
With your question on coin magic, the psychology is a bit different...when you make something disappear, there's an emotional "need" to see it come back. It's like playing an unresolved chord on the piano; it sets up a tension that we somehow want to see resolved. It's also like seeing the first 3/4 of a good movie and not getting to see the end of the story. So, if you make a coin disappear and don't bring it back, you set up a similar tension, and people look at you to try to figure out where it went...thus the, "Let's see your other hand" response.
When you're starting out, try to pick routines where the coin disappears and then reappears in another place. This resolves the tension for the audience, and you won't be challenged on that point. (They may challenge you on other points, but that's a different discussion.)