It's an one upmanship, Wilson was telling the league and other QBs that he had the whole playbook memorized. In theory, if one has the whole book memorized, it's quicker to just pull data out of memory than having to read the wristband, that's what Wilson was trying to project.
In his case, he often spent MORE time pre-snap, in the huddle, and often caused delay of game penalties. Of course, papa Pete took the blame for all the 5 yarders, for that reason, Pete made the "resistance" commend, he took all the blame because Wilson wanted to show off.
Is it possible to memorized the play book? Well, concert pianists memorized all the notes for multiple an hour or so long concertos, so I would think it's possible. How did the pianists do it? I used to enjoy free music at the Juilliard, as those students practice 8-10 hours a day over the same notes, day after day. By the time they stepped on the stage, they have played those concertos hundreds of times.