Ask: Do you still find any benefits in using handwriting?

I tend to program with a pen and a pad of graph paper at my side.

I tend to program in a 'distraction-free mode', where my IDE covers the whole screen. I still need a place to take notes, to hold my to-do list, and to make simple diagrams of dependencies.

I do. The direct interaction with the pen, the aspect of drawing helps me immensely: I can pull that image from my memory much easier. Therefore, if I need to remember something, I'll write it down, instead of typing it.

Also, for communicating I find writing/drawing (whiteboard) a very handy tool (in the toolshed). There is the potential problem of bad handwriting, but I fix that by forcing myself to not being hasty.

Finally, there is the aspect of authenticity; that seems to be important: Many cafés and shops arguably use it to appear more humane.

The carefulness aspect I don't see myself. I can think while typing, whereas while writing my attention seems to be caught more by the task at hand.

I've taken notes in many math, engineering, and computer science classes, and after that I've attended many design meetings, schedule meetings, and brain storming sessions. In these settings typing doesn't work well and there is a distinct advantage in having good diagramming and math notation skills.

I find typing better for prose and prefer to program in a text editor.

I've had this discussion several times with the people running my children's schools (grade levels between 6 and 12). They have always been big on pushing technology in the schools and moving away from simple pen/pencil and paper.

My kids grew up with computers, iPads, and cell phones and so did virtually every other kid in these upper end schools. They didn't need to be pushed to use keyboards and didn't need instruction in typing, my daughter has typed faster than I can for years. But the schools, and many parents, were obsessed with the idea of being modern. I tried to explain that low resolution touch screens were inappropriate for taking math notes past simple fractions, but of course, I couldn't change their minds.

I felt the use of technology in the schools often hindered instruction and learning. Naturally, there is a place for it and I was happy that my senior was required to prepare her math projects using Sagemath and LaTeX.

I've tried pretty much every to-do app out there and none of them beats a sheet of paper next to my keyboard.

Not really. I took notes by hand in my engineering classes in college, and on my laptop in my non-engineering electives (where I didn't need to write equations or draw diagrams). I didn't notice a significant benefit to handwriting in understanding the material. I still had to spend time reviewing my engineering notes afterward. If anything it was possibly more distracting trying to maintain legibility and neatness on top of paying attention to the prof.