In that regard, I think Jack is actually more troublesome and worthy of a few bullets than Mr.X, especially on Madhouse. Jack can actually run faster than Ethan and when you down him with a few shots, he stays down for a few minutes.
On the other hand, MR.X is slower than your characters and only stays down for 30 seconds. It's not worth (unless you need a quick run in a licker corridor or something. Mr.X is only a problem when you're trying to avoid him AND other enemies, but since I kill anyone I encounter inside the RPD, MR.X mostly chases me through empty corridors, so it's easier.)
I do pop a few shots at him when playing as Ada (if I have any ammo left), but it's just for fun.