First of all, it is not the case that "who" cannot raise over "did" in T (or more precisely - over the tense affix), because it does so when moving from Spec-VP to Spec-TP anyway (under the VP-internal subject hypothesis).
Second, X-bar theory itself says nothing about the constraints on movement; it simply states how the structure is organized - basically that every head has a bar-projection and then there is a specifier and a complement.
Third, Doubly-filled COMP filter uses the conception of COMP present in 70-80's, where both wh-words and complementizers like "that" both were of COMP category, that is C. So it does not really apply to cases where there is a wh-word in Spec/CP and "did" in C.
Now back to the main question - why?
Radford in his 2006 textbook "Minimalist Syntax Revisited" suggests that wh-words are attracted by an edge feature [EF] to Spec/CP and tense affix T is attracted to C by a tense feature [TNS], both of features are part of C. He then refers to Pesetsky & Torrego's analysis where wh-subjects can bring [TNS] with them when moving from Spec/TP (unlike wh-objects which never pass that position) and thus satisfy both [EF] and [TNS] of C in Spec/CP. Another option is that wh-subjects never really possess [TNS] and that [TNS] in C simply "needs" to attract something from T or its projections. In wh-object questions [TNS] can only attract whatever is in T and not the subject that is in Spec/TP because Spec position of C is already occupied by the wh-object. In wh-subjects cases, though, both [EF] and [TNS] would be satisfied by just moving a subject to Spec/CP.
I'm not aware of any other analysis of this and honestly I would be very unsatisfied by the one above since it posits the [TNS] feature which has no justification and is mostly unneeded in the analysis of wh-movement in other languages.