Repetition is mastery. When I played in a casino showroom relief band, one of the shows we did was a set piece at one of the showrooms. It was about an hour of music, in 4 segments. The short acts (comedians, magicians, dog trainers, etc.) between segments changed every 2 or 3 months. Very showbizzy and almost cartoon like. I played that show twice every Wednesday night for 4 years. By the 2nd year, I no longer had to look at the music. I just turned each section over and went on autopilot.
At one point someone in the section suggested counting Eb's in each part. So we all took a pencil and wrote the number on the top of each page. There was a question about whether we should use cancert pitch or written, but we decided on written. My part had alto and soprano sax, clarinet and flute and piccolo. The other alto had the same minus the soprano. Both tenor books had flute and clarinet, and one had oboe. Bari had bass clarinet, clarinet and flute. So we earned our keep. Lotta Eb's...
The guys in the regular band, who played that show 6 nights a week, asked about the numbers at one point. One of the trumpet players in that band then made a total for every note in his part. I pitied those guys, I was once called to join that band and turned it down because I knew my drug bill would endd up exceeding my salary. Several members of that band had nervous breakdowns. It was not horrible music, but it wasn't great either. Some of those guys played that show for its full run, which ended up being about 8 years. I don't know how they did it. But hey, they all had houses and cars...
I know the New York Broadway musicians, who often have a run of several years. can send in subs. It's part of the union regulations there, they can send in subs up to 50% of the shows. This allows them to go out for jazz gigs, or tour with a rock band or something. The casinos in Reno had no such policy, so those guys had to tough it out. I did sub in that band occasionally, if someone was sick or something, but it was unusual for guys to take more than 2 or 3 nights off a month.
So yes it's possible to memorize written parts. I was not the only one who did it. But there is a price to pay.