Yeah, that'd be my argument too; as I've never seen it done any other way.
Again, never happened IME.
Here the GM will often spend a long time (as in, many months) in worldbuilding, rules wrangling, and other various prep before even getting to the point of inviting players in. And even in cases where the pre-game prep has been quite short (as in, a few weeks or even less) it still comes down to a GM inviting players in.
Closest I've ever come to this was when I was running a game and another GM took it over more or less on the fly with the same party, PCs, and backstory; with me becoming a player.
Yeah, this has been my experience as well. When a campaign ends, we ask "Okay, who wants to run the next game?" The new GM will then propose what they are interested in running (or poll the group, if they don't have any ideas).
I'm not suggesting that there aren't groups that do so differently, just that it's never been the case for any of my groups.
If this occurs, often the notes the players took will be adequate, won't they? I mean, they're not going to try and leverage stuff they didn't know about or have forgotten about.
If everyone's memory is a bit hazy (that happens sometimes at my table) then a collective conversation can hash out the details.
It's less than ideal if you're trying to build long term story lines but might not remember an important detail in the moment. For example, in one of my groups two of the players went on their honeymoon recently, so we didn't play. There had been some scheduling issues prior to that as well (Superbowl, etc.) so last weekend was the first time we gamed in over a month and I was really shakey on the details.
Thankfully, I was able to skim over my session notes and remind myself of everything that had transpired that I consider relevant to the campaign. If a player had taken the notes, they might not even have been available to me between sessions, and even had they been it would have been totally up to fate whether they'd grok'd all of the relevant details or skipped something that seemed trivial then but would bear fruit down the road (I like to use foreshadowing).
For example, in the session before last they met an old miner 49er NPC who I made up on the spot. The party paladin took a liking to him, and after a brief conversation, gave him a 50 gp gem to fund his next expedition. They're only 3rd level, so that's a lot of money to him (he's still saving for plate mail). A month of two down the line though, he's going to find that the miner has hit it rich, and is quite grateful to the paladin. I'd never remember such a minor detail without my notes. The paladin player might note it down, but if another player were taking notes they could easily think a minor NPC like that were merely set dressing.
There are some tasks that I might consider offloading to my players because they aren't critical. Like initiative. Although I wouldn't actually offload initiative because I have a streamlined system that wouldn't benefit from it.
Never my notes though. In a real sense my notes are my game (or at least a very significant portion thereof).
I suppose it is fundamentally a choice, but to me it is a choice between running a better game and a worse game, and that's really no choice at all.