Been doing this for about a year, and I've noticed that writing down every idea does seem to have increased the generation rate of new ideas -- but that's not a bad problem :)
Two other benefits from carrying a notebook:
1) I've never been good at placing events in time, so noting significant events and the date helps me retain a life timeline of sorts. If particularly inspired I might note a thought or feeling about the event, but never more than a sentence. This is the closest I get to journaling.
2) Jotting down a note on paper appears to be more socially acceptable than taking notes on a phone. Typing on my phone has the appearance of ignoring the other person, and giving an explanation can derail the conversation. A notebook is self-explanatory.