I'm a little confused here, why are we talking about the JASSM? One, it's a subsonic missile, it'll be very vulnerable to CIWS using optical/IR guidance. Two, it's better to attack via multiple modalities than just sticking to one. Right now, China doesn't really have the ability to use missiles like the YJ-12 because no launch platform can get close enough. The point of the JH-XX would be to make that possible. Not only that, if it can launch at supersonic speeds, it can launch YJ-12 from an even longer distance. Another option is to launch an upgraded version of the YJ-12 that has the same range but can fly faster since it'll be launched with a higher initial speed and altitude than what the H-6 can achieve. Yet another option is to launch a higher quantity of short range sino-JASSMs since they'd be much smaller than longer ranged ones that a H-6 would need to carry. This would potentially decrease reaction time.
Being able to penetrate closer to a CBG and come back alive can open up a lot of possibilities. None of them is an "assassin's mace", but that's a lot of options offered on one platform.