My computer goes with me everywhere and is ready as soon as I open the lid. Unless I forgot to charge it.
How is paper not accessible? Do people not have note paper? What about junk mail? The last few pages of a book? You can make a scale ruler with any uniform markings.
It's one thing to draw a rough sketch of a part, and have someone else do the creative effort of turning it into an object. But quite another to specify in exacting detail how that part should be, so that given to several manufactories you would get back parts that are even remotely interchangeable. In that way it's a lot like the difference between a specification for a computer program, and the actual program.
When designing parts I often use pencil and paper when in an initial meeting with stakeholders, to quickly demonstrate ideas. But these sketches are not analogous to the real thing. They simply represent a direction work could be done
Pieces of paper are also likely to shift if you need to move things around frequently.
In a small apartment, surface space could be limited.