"I'm also way faster on a keyboard"

This is sort of the point of pen/paper - slows you down, makes you more contemplative. Plus, with a little practice I'm sure your handwriting would improve.

I practiced through my whole childhood and teens in school, it probably only got worse over the years as I managed to write faster with less care.

Few weeks ago I was at a party and had a moment of inspiration so I took a pen and paper to write down some poems. Barely I could read them later, let alone anyone else.

I imagine the inebriating substances often consumed at parties probably didn't help either

Yup, but I checked and I'm still terrible at handwriting :)

Adding an index takes care of the searching problem. Just a bit of extra effort that the computer normally takes care of for you.

I would say it takes care of the categorization problem. Searching, not so much, unless you spend an unholy amount of time maintaining your index.

Partly it depends on the kind of writing/brainstorming I'm doing. I make lots of drawings in my notes, which is hard to do with a keyboard only app. Graphics tablets, even my Cintiq, which I use for actual drawing, don't have the responsiveness and clarity for note taking, diagram doodling, storyboarding, etc.

Plus, and this the real killer, the start up cost in time of using a tablet and graphic stylus are enormous compared to having paper and pencils handy on my desk. A cheap memo pad in my brief case is also handy. I've tried using my phone, but keyboard input on a phone, while I'm sitting somewhere away from office requires a minimum dedicated effort.

A lot of stuff gets lost when you have to overcome those startup costs. Even unlocking my phone with the thumb sensor contributes to me _not_ reaching for my phone when I've had a thought.

Same, it feels too analogic.