To me it is remarkable how a social service of their magnitude has managed for so very long without having a proper web based service. In my narrow minded web developer view, I must admit, the web is where you start building your product before branching out to whatever other mediums makes sense.
In some cases I would build an API first and then a web layer upon that but taking it mobile first, in the most rigid definition of the phrase, could definitely simplify and speed up development.
Instagram success just goes to show how important the product medium fit is. Thanks for broadening my technology horizons, Mr. Systrom!