I'm assuming the model you want here isn't paying for demos, although that is a valid way of interpreting things. Instead you want games to be fragmented.

The problem with this model is the issue of fragmenting a game.

This model encourages 3 bad things.

The first is that developers are forced to make games with this approach in mind. Now story driven games have to be episodic in nature, or risk backlash from people who only bought a small segment. A game like Xenoblade Chronicles would suffer since people would hate the first segment's tutorial taking up a huge chunk of time/the story.

The second issue is bringing making the ios app microtransaction model a standard. Capcom already does this to a frustrating amount on the app store. Pheonix wright games let you try 1-2 cases, and then pay a certain amount for each following case.

The third issue is managing reviews. Do reviewers now have to compare sections of a game to other sections of other games? It's would be weird to hear "halo 5 part 3 had a slightly better story segment than fallout part 1, but the multiplayer in halo 5 part 3 was comparable to black ops 3 part 2." Also, seeing ads would be weird.

I would just prefer free demos to give people a feel for the game, a $60 game to have people play through the complete experience, and dlc to have the people who want more satisfied

No thank you.

I am perfectly ok with unplayed games sitting in my library. I know that I will eventually play them.

With this method, I would have to buy the game as I advance through the story. I really don't want to be thinking about money as I play through a game. I don't want to constantly evaluate a game to determine if that last section was good enough to buy the next section.

The other issue is what about sales? A lot of the games in my library were bough on sale. Seems impossible, or at least difficult, with this setup.