I strive for something more as well, but even provoking emotion is very difficult for me as a designer.
Maybe I should have said "comparatively easy", or just "not the holy grail that we make it out to be".
Back on the topic of interaction, a teacher once told me about his first time using a computer, and learning how to use a mouse. A friend was facilitating the process, and had him play solitaire. At first he was just focusing entirely on using the mouse, with his friend guiding him. Without even realizing it, he eventually started focusing entirely on the game. Once he stopped asking about how to use the mouse and was instead just talking about the game, his friend told him he had learned how to use a mouse.
Kind of rehashing what's already been said here, but:
I think that story translates to the inner level of interaction within the game space. When you first start playing a game, you focus on learning how to move around and interact with the space, and how the space reacts to you. Eventually, you focus entirely on simply experiencing.
This is not uncommon in games, but the problem is that the supposed Laws of "good game design" revolve entirely around extending that initial learning, turning it into an addictive process which is extremely detrimental to anything outside of itself.
Learning how to use a mouse may be engaging, but that's not the goal.