>When an automated script that alternates pressing up and right and left every hundreth time can beat the game, then well, that's broken.
From my experience, this greatly overstates the "exploit". In 2048 you get to maybe 128 this way typically before you can't move up/right any more, then you have to start thinking after the left press. Basically whenever you slide away from the "preferred" corner, supposing your plan is to slide back promptly, there's always a chance that a random spawn gets in your way and complicates the plan. Getting to 2048 on the first try doesn't sound like a modal experience at all. (Of course, most new 2048 players won't have had the experience of developing Threes first.)
For that matter, the developer talks about how rare it is to see a 6144, but doesn't seem to acknowledge that reaching a 4096 in 2048 is far more difficult than reaching 2048.
At any rate, it's not at all immediately clear why having the player join 1+2 first before making blocks of 3*2^n, should noticeably improve the gameplay over having only powers of two. So IMO it's not that the gameplay of 2048 is fundamentally less interesting; the implementation just sets a lower standard.
(Though for what it's worth, I've wondered how it might go with the Fibonacci sequence - allowing 1s to merge either with 2s or other 1s.)