You're failing to understand game theory here.
What good are nukes if you are not willing to use them and let others take what they want.
By having a very real threat of nuclear escalation you keep others at bay. That's how the US was kept out of cuba, that's how Russia was kept out of western europe.
Here, it's a very real threat of escalation:
- if China invades, US escalates conventionally and wipes out what it can. (conventional US missiles are not that far from tactical nukes, US navy will easily wipe out Chinese navy)
- Then China can escalate further by attacking US forces via land-to-sea missiles, aircrafts, etc, a few sunk aircraft carriers and you'll see the US out for blood.
- tactical nukes will likely be used by any side if it loses too badly.
- US could always do some risky air-strikes against Chinese leadership and close the war that way (or nukes start flying)
- China can't really reach the US mainland that easily and US has quite a few anti-missile forces off japan and on the mainland.
- at this point, it's survive who is best prepared. I'm assuming US will come off a lot better then China.