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Regarding the first point, that's precisely the idea – traveling shouldn't be easy. Consequently, you can present it in a way that even transferring a single creature between worlds is something truly significant, and in fact, it has only become possible relatively recently, perhaps within the last few years. And while some random travelers might have had some influence on certain worlds in the past, overall, it should remain something new and unexplored, with the characters being almost the pioneers in this field.
Then, of course, there are two problems: either all the players would be from one advanced faction, or at least from one organization, like "the chosen ones."