Designers that don’t care and don’t take into account all of their constraints are simply designers who don’t care… and mediocrity is the hallmark of a designer’s lack of attention to detail and not a byproduct of color choice.
The number of colors or lack there of is completely irrelevant to producing a good icon. The foundation of good icon design since before digital devices has been the crafting of a distinctive silhouette and that is even more important when it comes to a logo mark for a product’s identity.
If your icon does not function well in a single color on a solid background then your icon does not function. As products spawned in the early app markets slowly become brands of their own we’ll see this happen more and more.
Your Instagram example is a perfect illustration of this point…
At first, the Instagram app needed to to communicate to users what it’s purpose was but now it is so ubiquitous that the product has obtained verb status and it no longer needs to sell the idea of photography but rather the idea of “Instagramming.”
As the digital world becomes more complex the images we use in our interfaces need to become less complex and white or not… whitespace is the key.