I think what you mean by the first sentence is "most of 2048's fan base enjoys it because it's fun".

Your back and forth strategy doesn't work as you get to the higher point levels in 2048 btw. It certainly may get you to 2048, but not really that much further past that. The fact that the ideal strategy changes as you get to 4096 and 8192 is something that makes the game more fun to me.

If you like Three's better that's great, but like I said, I started with Threes, got addicted to it for a while, and then moved on. I got addicted to 2048 for a lot longer than I did Threes. It's not a matter of one being free or more accessible. 2048 is simply more fun, which is another way of saying it's a better game.