EDIT: Ah, wikipedia explains that the two X chromosomes in a standard-issue woman come from the mother and paternal grandmother, and then ... "Early in embryonic development in females, one of the two X chromosomes is randomly and permanently inactivated in nearly all somatic cells (cells other than egg and sperm cells). This phenomenon is called X-inactivation or Lyonization, and creates a Barr body. If X-inactivation in the somatic cell meant a complete de-functionalizing of one of the X-chromosomes, it would ensure that females, like males, had only one functional copy of the X chromosome in each somatic cell. This was previously assumed to be the case. However, recent research suggests that the Barr body may be more biologically active than was previously supposed." Which must be related to the EXITS that the OP refers to.
Being a male, I'm troubled by the fitness of the Y-chromosome over the generations. It seems to me that it can only accumulate errors and mutations. However, I suppose the same could be said about the mitochondria that come exclusively from females. This partial double-X scheme seems like a useful way of mixing up traits intrageneration and maybe strengthen healthful cell behaviors.