Well I have to disagree.
If this intercontinental HGV was developed in isolation, then I would agree with your assessment that it would make most sense from a nuclear delivery standpoint.
However, in the broader context of China’s new ICBM silo fields; continued upgrading and expansion of its road mobile ICBM force; advanced stages of development of its H20 stealth bomber and ongoing modernisation of its nuclear submarine fleet, including SSBNs. Well using this new HGV as a nuclear delivery option would seem distinctly overkill.
Not only that, but by making it nuclear, China would also effectively deprive itself of its newest, and as yet, only effective conventional strike option against high value targets on CONUS itself.
I would say that it would make very little sense for China to use this HGV for nuclear delivery, when you consider it should have MAD fully covered by the massive expansion of its conventional nuclear delivery triad by the time this new HGV becomes operationally deployed.
OTOH, having the means to reach out and strike, conventionally, at basically any target it wants on the CONUS will be a complete game changer in terms of both political and operational dimensions for China and America. And will drastically increase the costs to the US of any direct military engagement against Chinese forces, which will reduce the chances of the US deciding to get into the fight directly to start with.
Hell, even from a strategic nuclear standpoint, it would make far more sense to use these new HGVs conventionally, since the US would be compelled to expend its limited BMD interceptors trying to shoot these down in the lead up to escalation to nuclear even if it knows full well the HGVs are only carrying conventional payloads.
This depletion of its BMD capabilities before escalation to nuclear will both serve as a further deterrent for the US to go nuclear; and failing that, will make the inevitable Chinese counterattack all the more successful.
So, my impression is that developing the ICBM ranged HGV in context of China's increase in its overall nuclear arsenal size+credibility, is why I think the IC-HGV system is likely to be nuclear oriented.
The increase of China's ICBMs, new silos and DF-41s, upcoming new SSBNs and stealth bombers, imo all suggests to a desire to develop a more credible and capable nuclear deterrent and one which is more difficult to defend against.
An IC-HGV system would be entirely consistent with the pursuit of a more credible and capable nuclear deterrent system, in light of US BMD pursuits at all levels of the spectrum (including against ICBMs).
Putting it another way, an IC-HGV system is being pursued to ensure that if the effectiveness of China's conventional ICBM force is diminished due to an emerging BMD capability, that a resilient nuclear delivery method will be retained to ensure vulnerability.
If you are suggesting that the IC-HGV would have a conventional role and would be used against CONTUS as a conventional strike weapon... That is a very, very niche capability and frankly for it to be viable, it would require both China and the US to fully understand that launches of such a weapon cannot be interpreted as a nuclear attack.
It is not impossible, but I think that the integration of an ICBM ranged HGV as a conventional strike weapon against the US would be such a massive reorientation of PLA of assessments of risk and strategy, that we need some kind of significant hints to consider it to be a likely use of the weapon.
That is to say, at this stage I think the most reasonable null hypothesis for this IC-HGV weapon is that it is intended primarily as a nuclear delivery system.
I am certainly open to the idea of it having a conventional role, or even it being exclusively conventional in relation to nations like the US, but I think it would be a significant enough departure against existing PLA strategy (seeking the capability to conduct conventional strikes against CONTUS, and with intercontinental ranged weapons no less), that we need some level of hint or some allusions to suggest that is what they are pursuing.