I've been a replacement SM for a show I didn't know, and I moved from ASM to PSM within my current company - so I've called a lot of the shows I used to ASM.
As loebtmc points out, the "1-2 show shadow, then 1-2 shows observed calling" was what I went through. I watched the show once from the house to actually see it and understand it. Then I sat next to the SM the next night and watched her call. Then I took over for her, having her watch me. I then took over for the rest of the run. It was actually my first AEA calling experience, and it wasn't that bad. Granted, it was a fixed set with 2 actors, but walls moved, there were sound and lighting cues, so there was stuff for me to do.
For the ballet company I work for, on our more complex shows, we make what LizzG refers to - we call it our Cue Track. We pick one performance, and while you have the video and audio of the show, you also get ALL headset chatter for one channel. For our large shows that include pyro, rail, deck, spots, fog, and symphony - it's helpful to hear all of the communication. It can get confusing at times, but that's why only the Electrics channel is selected to be recorded, as the PSM always talks on that channel and adds the Carpentry channel when necessary. Back in the early days of our company, the ASM would call spots while the PSM would call Deck and LX, which is why you'd want to hear all of the electrics channel vs. just one person.
For myself, I've ASM'd and PSM'd Swan Lake, Giselle, Pirates of Penzance! the Ballet, and several years of The Nutcracker. There have been times when I can still hear the cadence of the previous PSM calling the cues - especially in Nut. I will say it is a completely different way of thinking (at least for me) when moving from ASM and the deck-minded ways to PSM and the big picture calling on the same show. Granted I had some of the calling sequences engrained in me from 5 years of listening to the PSM call the show, but there were some sequences that I was not familiar with, because I had several other things going on deck-side so I didn't have the opportunity to mentally memorize what the PSM was saying.
Yes, I think it's beneficial to move from ASM to PSM on the same show, but it really derails you as it's a completely different way of thinking (at least in my ballet world). I honestly think it's easier to pick up someone elses show as an outsider, because you don't have a track stuck in your body and mind. There are still times when I hear certain musical cues or see black outs that make me think of my ASM track and what I'd be doing right then, and I have to remember to forget about that - there's a new ASM doing it now - and I focus in on my PSM track.