This is so important. I feel most note taking apps approach note taking the wrong way: organization first, ideas later. Most of our notes are random and the only real organization they can fit into is time.
I have recently launched a note taking app [0] that keeps this in focus. In my opinion, "organizing notes" is often done after "writing notes" and that is how the app is built.
1. Note taking is a fast activity - you can take notes from any where in your phone, opening the app is fast, the steps to actually writing a note are frew, the note editor is uncluttered and stays out of the way, and the app works anywhere you have a browser & an internet connection.
2. Time is a first class citizen: all notes are sorted by date created, grouped by modifiers like year, week, month & alphabetical.
3. The app doesn't force you to organize your notes i.e., there's no special distinction between organized and unorganized notes. Some apps put unorganized notes in a specific folder or tag. Not so with my app. The focus is on writing notes; organization comes later.
4. Recalling notes is currently not the most amazing thing. There is full text search, however I feel like that's not enough. Things like similarity search (based on tags) or advanced filtering are yet to be implemented.
I think all these fit well into the incremental note taking system. However, that's a coincidence really.