I don’t think US politicians care about 3M lives once they would have decided to begin a nuclear war. 300M is enough, perhaps.
Well there is a reason why China has road-mobile ICBMs.
Also, the US DoD assumes that their warheads have a reliability rate of 80% during the Cold War. Assuming that they are right about their own warheads and that they will deliver 2 warheads against 1 silo, there is a 4% chance for each target silo to survive. Thus, in the 300 silos that came under attack, we can expect 12 silos to survive and retaliate. By launching ground-burst warheads and targeting cities near agricultural centers, China can contaminate American farmlands to cause a famine over the next few years.
They can claim they’re OBS. US nuclear doctrine doesn’t tend to fight back immediately once the alert is triggered.
In your proposed case, the US launches a first strike with bombers. This suggests that the US is already willing to use nuclear weapons first. In this case, the decision to launch nuclear missiles against China has already been made. Any additional attacks are only follow-up strikes instead of a whole new political decision. In fact, I think in your case it is implied that the American leaders are expecting (or even willing to accept) a Chinese nuclear retaliation. By launching OBS, China is not gaining significant strategic advantages. The intention to retaliate is clear regardless of what system has been deployed. There is no additional advantages offered by OBS (compared to FOBS in this case anyway).
In that case there will be no need to rely on OBS as well. Just build more warheads and missiles.300 missiles are enough to beat BMD even without any special design.