Great idea and great presentation but it's not ideal that pulling blocks is kind of awkward and limited (e.g. can't move blocks to the edges, and often end up slightly too close to a block so the pull fails) compared to sitting around just smashing appropriate blocks which is easy but less interesting.
I suggest allowing pulling at close range to just shift you back a space, and giving a few frames of leeway to pull a block after it makes contact with the ground (like in real Tetris).
Not sure what could be done about the edges without allowing either pushing, or player movement outside the play field. Maybe just have the block spawning system cheat for you by generating additional edge blocks where needed (if you're not already doing so)?