There are a lot of ranchers and larger breeders that do not let their chins out for playtime. They handle the chins and they keep them happy, but they don't have the desire or time for out of the cage playtime. It does not impact the chins' happiness in any way.
Chinchillas will get enough exercise regardless of getting out of their cages or having wheels. They do not atrophy or develop other issues simply because they do not get out. For the most part chins see their cages as safe, comfortable places to be. It isn't torture to keep them inside. No one should make other chin owners feel that way if their chinchillas do not get out.
None of my chins get out every day. There are a lot of chinchillas here and that would be absolutely impossible. Some chins get out four to five times a week, some get less and some do not want to come out for playtime. I raise chins for pets so I have to allow them to understand about getting out of the cage. That means that I must take them out and let them run in preparation for a new home, I don't want them to stress out.
As for the amount of time out of the cage, they don't need an extended period of time out. 15 minutes will usually suffice, more than 30 to 45 minutes isn't necessary. They are most active the first 10 to 15 minutes of being out...after that they are just looking for things to chew and destroy and to escape to non-chin parts of the home. Too much playtime for younger and some older chins can result in instances of hypoglycemia, as well.
I don't think you are doing the wrong thing keeping the chin in the cage and handling her a bit here and there. If that works for you and your chin is a good pet for you, it's fine. Most people want to take the chins out and let them play and that's alright, too. You need to do what you are comfortable with doing!
One thing that I would recommend is trying to handle her more and more and get her used to it. Before letting a chin out to play regularly it is so important to have the trust of that animal. If you have a fearful chin that doesn't want you to touch it at all, it will be very difficult to wrangle that chin and get it back in the cage when playtime is over.