Something that you're forgetting to consider in your analysis is that while Instagram is a mobile first company right now, there is demand and a place for them to have a stronger web presence. There have been other media outlets to speculate on this topic but obviously before the acquisition they did not have the resources to dedicate time to a better web experience. Now that they will be given significantly more resources they will now be able to deliver such an experience. As you've noted web advertising is far more effective of a method and therefore will be an area for revenue generation. Instagram would also have the possibility of creating a platform for people to sell their photos or have them made into art like other companies do right now. Things like promoted pictures could be implemented much more easily to work with brands. In the same way that Facebook generates a primary amount of its revenue while leaving mobile untouched for the time being I believe the same can be done for Instagram. Mobile is the bread and butter for Instagram and still will be as it continues forward but a web based experience can greatly help the company both grow its user base and grow revenue.
Basically what you're saying is that Instagram actually does have the potential to make $1B. Care to ballpark some numbers as to what income your suggested methods of monetization would actually have to produce to make Instagram be actually worth $1B?
Something is only worth what someone is willing to pay.
Exactly. Beyond everyone's need to rationalize why Facebook paid that much for Instagram, it's clear that Instagram is worth $1B to Facebook, because that's what they paid.
The relevant question is not "what is Instagram worth" but rather "what should it be worth." That is, we already know that Facebook values Instagram at $1B; the question is whether that valuation makes sense.
But "what should it be worth" can be debated until you're blue in the face and still have no real outcome. What Facebook paid is a fact, not speculation.
For all you know, Google is kicking itself for not making a $2B offer to them, because Google Plus could use all the help it can get.