Writing parts definitely helps ingrain the song by forcing you to listen carefully to the drums, but usually results in using the chart as a crutch. That's not a bad thing, I do it on occasion mostly for arrangement purposes. But knowing the song in your head is much more useful, and if nothing else, demonstrates more of a commitment to the music to the other players. Is that important? I don't know, but it couldn't hurt! I get songs thrown at me all the time, and I tell them (afterwards) that I've never played that song before, but I know it. That always amazes them that I could recall it - often with the original fills - out of thin air.
I don't know those songs because I wrote them out at some point in my life. I know them because I'd heard them over and over at some point, and listened carefully enough to call up the parts 20 or 30 or 50 years later.
I've told this story a few times, about sitting-in with a group for the first time about 15 years ago, and playing the Animals "We Gotta Get Out Of This Place". Right after "girl there's a better life, for me and you" there's a little tom & accent breakdown leading into the next verse. The leader turned around and gave me a funny look, I thought he was mad about something. Maybe he thought I was too loud or had sped up? I asked at the break what was up, and he said he'd only heard that part on the record, no drummer ever played that with him before! Mind you, I'd never played the song before at all, and didn't get a set lists prior to the gig in order to study it. So, no chart, no nothing. But I knew how it went, because I'd heard it almost 40 years ago and it was in me, just waiting to be recalled at some point.
Bermuda