If we look at the geography of the USA there is an ocean of water to its west and east. There are 2 very weak nations to the north and south. There are No military threats anywhere within a 4,000 km radius of its borders. Because of this the US military can focus 100% on long distance power projection and ignore short range defense.
China has an "opposite" geography.
There's at least a half a dozen nations, relatively close by, that can potentially become hostile in a future war.
It makes no sense to be preoccupied with the idea of running 12,000 km across the Pacific ocean to hit a long distance target when you literally have a half a dozen rivals that can hamstring your efforts before you even reach 4,000 km out.
I don't understand the fascination some people have with "hitting" the USA.
How come there isn't a fascination with China convincing all the east Asians nations to turn their backs away from the USA and instead chose military neutrality? If China succeeds in this, then the USA loses its military influence in Asia and must compete on its economic merit which we all know isn't very good these days.
I think Chinese geography is more similar to US than you think. Lets see whats around China:
Russia: Preoccupied with Europe. Friendly relation.
India: separated by worlds tallest mountains and neutralized by Pakistani proxy.
South Korea: Neutralized by North Korea. Minor nuisance.
Taiwan: Minor nuisance, and the first one to go down in a conflict.
Japan: The only relevant threat and the military is built around fighting Japan and US combo.
Others: Vietnam and etc are irrelevant, less relevant than Canada and Mexico that you dismissed.
Essentially China is an island. With the exception of Russia there is no relevant enemy with sufficient border access. The closest is Japan across the sea. If Japan is shut down with naval dominance, then hitting US is a reasonable next goal.
The importance of hitting US is not that everything should dedicate to hitting US. It is important to have credible threat to US main land that disrupt American strategy closer by. US would need to be in constant air patrol, deploy SAM networks, relocate sensitive industry, and those effort would divert resources from regions closer to China.
Technically a couple ballistic missile could do it, but those exhaust way too quickly. H-20 would make these harassment much more affordable and constant. Not to mention, just because H20 can hit US mainland doesn't mean it cannot deploy tactically against targets closer by. Who is to say H-20 cannot lob a few heavy anti ship missile to targets west of Hawaii? Or drop a few tons of glide bombs on Taiwan and Japan once their air defense is neutralized?