Many people interpret quality of design as an indicator of content or product quality.
To address your particular question, depth creates a more realistic and visually interesting representation of information on a screen. It can also serve to indicate the priority of information on a page. If depth draws your eye to or away from a particular element, it can help to achieve the designer's goals.
I am just speaking my mind, what kind of things prevent me from trusting others despite of their benevolent intentions. Time and again, I've been bitten by bad subjective advice - there is a lot of bullshit out there. Tread carefully, adopt what makes sense to you and ignore others unless evidence shows otherwise. That said, there are a lot of gems out there as well.
If the thing I am making is art and is subjective, then why can't I just be original? If a particular activity is totally arbitrary, then all bets are off.
Blindly following advice is why we as a society get stuck in a local optimum and don't try other things. Domain exploration and experimention, originality and authenticity are paramount to getting out of the local optima. Every once in a while someone does and they revolutionize the world.
Anyone who can draw knows what that means.
> Overlapping images is a great way to add depth to an interface and make it look more “designed”.
I don't know if this is sarcasm. No one is asking why do we need to add "depth"? What problem is "depth" of overlapping icons solving?
I would stay away from this.