This implies that you exclusively use digital tools, so my first question would be: have you tried using pen and paper for things?
It's really hard to give compelling examples of where pencil/pen and paper are going to be better than digital tools because everyone is different. If you want to try it out, I recommend simply keeping a pad and a pen at your desk and when you're stuck on a problem try writing something down. Whether it's mapping it out, quickly jotting down some assumption or thing you noticed etc. It won't be suitable for everything but there's something... visceral about writing with a pen that I find indescribably helpful in working through complex problems. This was how I got started with this process, at least.
For a more concrete example, I spend a lot of time in my current role thinking about high-level solutions to problems. Things that need to serve multiple different teams' needs, replace existing solutions (aiming to solve their most obvious pain points), sometimes have non-obvious simple solutions, legacy complex solutions that everyone is used to and just kind of accepts etc. These designs come from months of discussions with different people, thinking, theorising, research into existing solutions etc, but one thing I have found absolutely invaluable throughout this process is the pen and paper on my desk. My notebook is full of unorganised notes that I jotted down when a lightbulb came to me one day, rough sketches or mappings of solution ideas, brainstormed lists of features etc. Most of these don't see the light of day, but as they get refined they move to more permanent, collaborative (as necessary) mediums. I do this progressively by flipping back through my physical notes and reviewing/extending/transferring them as necessary.
> My notebook is full of unorganised notes that I jotted down when a lightbulb came to me one day, rough sketches or mappings of solution ideas, brainstormed lists of features etc.
This is to me the biggest benefit of using pen and paper, but it requires shifting your attitude towards pen and paper to treat everything you write as disposable. Just freely sketching out ideas and using paper as a place to dump thoughts without concern for quality, formatting, or even having them be cohetent, is probably the most productive way for me to solve problems - so much so that I have switched to using large post-it notes, rather than a notebook. The good notes stick around for a few weeks, and the bad ones go straight into the bin.
If I can express something through writing (as with the cases you mention), there is no faster, more convenient tool than a note taking app + keyboard. It's instant, archived, editable, and globally available (where there's internet of course).
If it's an idea that needs to be visually designed (shapes, graphs, space), I find that I can mostly do this by redefining the problem in a way that can be written down.
There's a small percentage of time where having a diagram is truly essential to my workflow. I'm not opposed to whiteboarding in these cases, but it's not as vital to my process as the author implies it is for them.
> indescribably helpful
I tend not to be convinced by things that are indescribable. What I'm understanding is that it's a tool that makes you happy. That's sometimes a valid enough reason to do something.
This implies that you exclusively use digital tools, so my first question would be: have you tried using pen and paper for things?
It's really hard to give compelling examples of where pencil/pen and paper are going to be better than digital tools because everyone is different. If you want to try it out, I recommend simply keeping a pad and a pen at your desk and when you're stuck on a problem try writing something down. Whether it's mapping it out, quickly jotting down some assumption or thing you noticed etc. It won't be suitable for everything but there's something... visceral about writing with a pen that I find indescribably helpful in working through complex problems. This was how I got started with this process, at least.
For a more concrete example, I spend a lot of time in my current role thinking about high-level solutions to problems. Things that need to serve multiple different teams' needs, replace existing solutions (aiming to solve their most obvious pain points), sometimes have non-obvious simple solutions, legacy complex solutions that everyone is used to and just kind of accepts etc. These designs come from months of discussions with different people, thinking, theorising, research into existing solutions etc, but one thing I have found absolutely invaluable throughout this process is the pen and paper on my desk. My notebook is full of unorganised notes that I jotted down when a lightbulb came to me one day, rough sketches or mappings of solution ideas, brainstormed lists of features etc. Most of these don't see the light of day, but as they get refined they move to more permanent, collaborative (as necessary) mediums. I do this progressively by flipping back through my physical notes and reviewing/extending/transferring them as necessary.