The times when I actually bother getting up off my butt and picking up a pen, I do notice a lot of productivity.. almost entirely because you can't click away to Facebook every minute, and it doesn't show you anything that reminds me of the fact I
could be scrolling dumb crap.
I spend a lot of time thinking about each individual letter and stroke to have any chance of legibility though, and was very slow even when I was practicing heavily as a teen(I heard GEDs were subconsciously scored based on penmanship, even though they're not supposed to, and wanted to give myself an advantage).
There's also a small security issue, Google can probably read Google Keep, but people I actually know can read paper if I leave it behind, so I wouldn't want to use it for any kind of private journal, unless it was something that never left the house.
It can also be lost and there's no instant sync, plus there's no reminder feature, so I wouldn't want to use it for anything critical, that's just making myself a single point of failure in my own life, even if the paper itself is reliable.
The productivity gains are noticable enough that it definitely does seem like there's real value there though, despite the extra work.
If I get stuck on a problem, I pull out my Boogie Board(Not quite paper but great for throwaway notes).
I also like to use my A5 binder notebook in meetings, especially if I'm new to a group, or it's a casual discussion that's not highly technical, almost as part of my wardrobe.
It gives transparency that I'm actually paying attention, not scrolling Hacker News, as opposed to a screen only I can see, and it doesn't break immersion if we're talking about a project that doesn't involve tech, like building something that's meant to feel old fashioned.