I remember when this happened, and I remember its forerunner, DnD Online. I played a month of that when it first came out, and liked it, but not quite enough to keep paying monthly. Turns out, most people thought the same way, and they couldn't turn a profit. Then they went F2P as an experiment, and started making money hand over fist. The trick was, the core game is all free. Quests, the world, you can get it all. The things you had to pay for were not essential to "the game". I played for a while for free, and it was legitimately fun, and I bought a couple small upgrades, nothing big, but I feel like I got my money's worth. After that, several other MMOs went to the same model, including LoTR, and both Everquests.
The model they went with works because I think a lot of people are like me in that they don't want to devote a huge portion of their time to a game like that, and paying $15 per month doesn't make sense in that case. But playing every now and then, and paying a little here and there means it'a a better value, and it's easier to pay the amount you're getting out of it. This causes a wider audience to come in, as they're not immediately blocked by something that isn't a good value for them.
It's not just 'Free-to-Play', it's an extension of the "pay what you think it's worth" model that has been so successful for things like music (Radiohead), stand-up comedy (Louis C.K., Jim Gaffigan), and indie games (Humble Bundle, Indie Royale).