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davidcyclebackAnother positive about a display case and ball cubes is some damaged is caused by long term exposure to dust and grease in the air. You case likely will help minimize this.
The three major causes of fading and exposure damage to art and memorabilia is 1) Light, especially UV light, 2) Extreme temperature & humidity conditions (do't want too hot and humid). Don't display your antique photos in the sauna and 3) Longterm exposure (ala years) to bad stuff in the air. You don't want to display your movie posters next to the french fry vat.
My opinion is using a UV protecting display case for your baseballs is a sound idea.
I looked into it once, and collectors can buy ball cubes that block UV light.
Autographed baseballs are funny things, because the sigs can fade and leather tone due to reasons other than light exposure. Sigs fade when they stored in a box. Problems include that that some inks and the leather itself can be unstable. If you think about it, writing with a dime store pen on an animal hide doesn't sound like the recipe for eternal youth.