Personally, I doubt that EPC is adequately organized to manage such transfers. And while I am willing to accept that some schools are more likely to counsel students towards a transfer than others - and that the schools less likely to recommend transfers may be more likely to receive such students - in most cases I want to believe this is unintentional. After all, if a student isn't doing well at a school, the well-meaning adults at that school may truly believe that the student will thrive elsewhere (as opposed to thinking only of getting rid of the child).
I also think that this conspiracy theory arises at least partially from the reality that highly-mobile students are more likely to be high-needs. If a family is moving a lot, the family is almost certainly having problems - financial issues, family violence, etc.
That said, I don't think it is controversial that some schools are more demanding on certain aspects than others. At least one school in the district strongly encourages red-shirting in Kindergarten. Others are extremely specific about their homework policies. This article notes that the school in question tells parents not to enroll unless they can be 35 minutes early every day.
In some ways, this is useful information. I personally am not a fan of big homework requirements and would not want to enroll at a school that had them; I would like to know about this in advance. District schools have different start times; school hours are something a family should know prior to enrolling. And the schools are not setting legal requirements; even if a school recommends red-shirting, it cannot bar entry to a child with a late August birthday.
Still, I think we need to accept that these school policies do impact who enrolls and who does not. And more broadly, I think we need to find better metrics for quantifying the percentage of a school's population that is high-needs - and use that information to better fund those students who need more support.