Perhaps this is a slightly different system , set after Madoka ? It might be that in this system , Puella Magi's go through 3 stages . Firstly , as a Puella Magi , Secondly , as a Witch , and finally assuming that they've survived long enough/somehow redeemed/ repent, returned to their human selves , with all it's implications .
Essentially , with Witch like powers , but without the draw back of insanity. In other words , immensely powerful reality warpers with their humanity intact - or as intact as their powers would allow them. Barriers created by them are extremely subtle and almost indistinguishable from reality, and within their barrier , their conscious will becomes reality.
Kazumi is essentially a Puella Magi - post Madoka rewrite of the rules. Which might explain why the connection is much weaker - the whole system was amended.
Alternatively , this might be a more advance system created by the Incubators , designed to ensure that Worlds last longer , and a more sustainable harvesting of souls can be effected. PM3 was essentially the prototype Alpha , this is the Beta.
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