I think it comes from the fact that there's a direct visual representation of the work you as a player did in the game that affects gameplay. It wouldn't have the same effect if the game wasn't essentially designed around it. Imagine if one bird appeared every 5 seconds as opposed to every time you collect one. It probably wouldn't be as impactful, because it doesn't directly correlate the you as a player collecting the birds.
Wow, this nails it on the head. And the snake example was perfect too.
So since it represents the consequences or results of your actions and choices, but has a heightened visual representation, is this a form of juiciness? It's not particles and explosions to show "I pressed a button", but it's followers and tails to represent "my accomplishments are building in number".
Katamari also has this effect then, but more than juiciness, all of these also affect gameplay. As you progress, your tool changes and grows visually to represent the changes in gameplay that accompany it, until you have a far more powerful and large representation ingame.
So it's not juiciness, but it's your tool growing in size and power, or maybe just size (and thus usually vulnerability) or maybe just power (is this more the awe side, since you don't have to worry about it? Journey's scarf does not add risk as it grows, but snake and katamari do)
Very interesting stuff. Thanks guys!