at point blank range: as you mentioned, j.mk whiffs on most of the cast crouching so I will assume that the discussion of j.mk only concerns its use as an IAD tool from further than point blank.
compared to j.mp, it does have the benefit of scaling your combo less (assuming you let j.mp run all the way that is). If you let j.mp run completely it's +16 on block, if you fastfall it it's +11 or +12 on block, so essentially the same as j.mk. On hit, j.mk is +12 vs +10 of j.mp (fastfallen), but the damage if you fastfall j.mp after the first hit is 150 for j.mp and 200 for j.mk, I would not call 50 damage a significant benefit. j.mp as you mentioned also gives you the option of letting it rock for multiple hits, which not only breaks armor but will also mess with pushblock timings since you can fastfall it on any of its hits.
Even compared to IAD j.mp I wouldn't really say IAD j.mk is really better, let alone compared to filia's other IAD options like IAD j.hp (less startup, more damage, and more + on hit and block) or IAD j.lp j.lk (2 hits so scales the combo more heavily but is SIGNIFICANTLY faster and more + on block, as well as being slightly more + on pushblock and since its 2 hits it's easier to react to being pushblocked out).