When the US was bragging about Prompt Global Strike, they warned nuclear adversaries could not assume it was nuclear... The US will assume it's a nuclear attack but who says they will be only used on the US? The US has plenty of other platforms to strike conventionally around the world. China doesn't. This would fill that gap.
An ICBM ranged HGV could certainly have a conventional role -- however, I believe its primary and initial application will be as nuclear delivery vehicle.
If the PLA wanted an ICBM ranged weapon that they wanted to be able to use against global targets in a rapid manner, against enemies that are not the US (and assuming they are thus not concerned about whether the US would interpret it as a nuclear launch or not -- which imo is a dubious assumption, but let's entertain it for the sake of discussion), then why don't they just use ICBMs as delivery vehicles for conventional warheads?
No need to develop hypersonic glide vehicles for that.
IMO, the reason why you develop HGVs is to pursue a weapons system that is more difficult to counter than traditional ballistic missiles (whether it's at SRBM, IRBM or ICBM ranges), and to seek a more varied means of delivering ordnance on target.
Against low technology/low capability enemies, they would generally lack any competent form of ballistic missile defense, so you can simply use ballistic missiles instead of HGVs.
In other words, I cannot see ICBM ranged HGVs being used against anyone but high capability foes at global ranges, and in such a case, I cannot see how such a weapon would not seek to overwhelmingly prioritize nuclear delivery as its primary mission.