The focus of this discussion seems to have honed in on the note taking thing. I want to highlight session recaps as a long-form version of note taking, but I will say I find note taking in game to be an unnecessary distraction.
Anyway, 95% of my 5e gaming time has been on the DM side, and I've made it a point to write a session recap my players can access between games. On top of this, I begin every session with a verbal recap, and single out a different player every week to lay it out. There's one player who consistently does a great job, but the others tend to be a little spare in their descriptions, and I often assist in reminding them of relevant details. Sometimes I tease them about it ("You skipped the part where Fernand almost drowned...") but it's never mean-spirited.
One thing I've noticed from the not-so-great-recappers is how they do an adequate job of relating events their own PCs engaged with, and forgetful about events they were not. This isn't surprising, of course, but I think it's relevant to the matter at hand. What may seem note-worthy to one player may not be so note-worthy to another. This is a big part of the reason why I do the written recaps, because as the DM I have a more complete perspective on which details matter to the story. I've been surprised more than once when a player remembers some throwaway NPC's name I didn't even bother including in the recap.
Earlier this month I returned to the player side of the table for the first time in over a year. The DM is one of the players from a previous game I ran, and he began doing written recaps much as I did long before I joined his group. However, he's now vested in 3 separate games and has a busy professional life, so I volunteered to do it for him/us... and I find myself struggling with the problem I described above, being tuned into my own character's experiences but a little shaky on others. "Was it the ranger or the druid who approached the strange woodland altar and provoked the woads into attacking us?"
All this is to say that, on top of being a distraction to do in-session, note taking by players isn't necessarily even reliable. Moreover, when it comes to recaps the DM has a more complete perspective and greater investment in the details, and owing to this, a greater ability to mitigate any dysfunction caused by forgetful players. As I apply this point to myself, it translates into an obligation to provide a written record to my players. YMMV