Freemium works so well because of the simple formula of revenue mentioned earlier:
On top, Freemium seems to be the only market that really works on Android, and I dont know if that is a matter of the demographic or what. You need simply look at the top grossing apps, and you will quickly understand why.
One of the problems with Freemium, is the ad supported market, at least on Android, is horribly broken
Number of people who visit * visitors who actually buy * buyer's amount they spend = revenue.
Because people are not fearful of spending money the first factor goes up. Since too many (paid and free) games let that sit around zero, perhaps getting into the hundreds, the freemium model immediately generally opens up revenue by an order of magnitude.
Players in freemium may have a smaller purchase rate (attach rate of maybe 0.005) but the amount paid per item is much better (often $0.99 per purchase). The 99.5% who don't pay will have a perfect attach rate (1.0) but the amount per ad is horrible (about $0.00001 per daily unique player). Having every player giving some revenue, even if the revenue is tiny, is much better than having zero revenue at all. Since the model increases the first revenue factor the offset is generally acceptable.
From an experienced business perspective it is not horribly broken, but instead seems very successful.
This isn't just limited to freemium. Purchasable addons, power boosts, etc are available in some $1 games on appstore aswell and on the PC pretty much every game has DLC for sale these days.
It is easier to get people to pay a little bit multiple times than to get them to pay alot once, and some people get far more willing to open their wallet once they've invested their time in the game.