Not sure if it is absolutely required that the dreamer of Level A not go to Level B but with the rules presented it would make sense that you'd probably not want to do that if you can avoid it.
As an example, even though Fischer's consciousness was on Level 3 (and then Limbo 4) his protective projections were still going after Yusef on Level 1 and Arthur on Level 2. If Yusef and Arthur had advanced down the levels with everybody else it would leave behind a group of deeply unconscious people to be slaughtered (under normal circumstances that would just interupt the mission, under these circumstances send everybdy to limbo).
And even though they didn't know Fischer had defensive training, they still knew they'd need to leave someone behind because the sedative required a simultaneous kick at each level and so someone needed to be there to coordinate it.
As for why it has to be the dreamer who stays behind, I don't think this is addressed specifically but the logic I see is: if the architecture for the level is in the mind of the dreamer, what happens to that architecture if the dreamer becomes unconscious to that level when he goes down one more. It doesn't seem illogical that it would either disappear completely making the next level down now Level 1 or it would become otherwise distorted beyond comprehension.
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