If that is the case, it would be wiser to shift to a counterforce targeting methodology and robust construction of missile defense, and literally begin armed reunification not with conventional missile salvos against US naval bases in the Pacific, but with a full scale nuclear strike on the United States.
The Minuteman III has a maximum range of 7600 nautical miles with MIRVs. This is more than enough to hit all of the DF-31 ICBM silos.
The Minuteman III does not use separate MIRV and "single" warheads. When the Minuteman III is talked about as carrying a single warhead, it is really the bus for MIRVs with 2 out of 3 removed. Whether carrying 1 or 3, all of its warhead configurations have the same yield.
You are correct these are real technical problems, but they date to the 1950s. The only submarines that really had this issue were very early Soviet SSBs, which had to surface to fire their missiles.
The Ohio class, as well as modern Russian SSBNs, are designed to fire their missiles in quick succession without drastically compromising the stability of the boat. This is achieved by firing one missile from the tube on the port side closest to the conning tower, and one missile from the tube on the starboard side furthest from the conning tower. This allows the re-stabilization of the boat to be achieved within about a minute; all 20 missiles could be fired in 10~ minutes.
That said, others have correctly highlighted that China's early warning capabilities render a disarming first strike unfeasible, regardless of the effectiveness of American systems.
That implies that China will never attempt armed reunification of Taiwan, because the US intention to potentially use nuclear weapons indicates the potential total destruction of China. China (the nation, not its nuclear forces) equally has no ability to withstand US nuclear retaliation.
Of course, the situation is not so, China has a very different approach to thinking about nuclear weapons. China does not need a huge amount of nukes because their only value lies in their political effect, not kinetic effect. Therefore, achieving parity with the US is unnecessary. The infrastructure that maintains America's 21st century way of life is very small, only hitting coastal cities and the two largest cities in inland states is necessary to bring about a collapse of US society. Even the existing arsenal is more than enough.
If you have a source of information about this "significant probability of failure" for Minuteman III and Trident D5 test launches, I would like to see it. The only reference to a failed Minuteman III launch I could find was from 2023; other tests publicized in recent years have been successful. The US Air Force and Northrop Grumman unfortunately do not disclose much data related to failures, but luckily, the US Navy and Lockheed Martin do. The Trident II has been test launched 215 times in total, with only eight of these flights failing. Five of these failures occurred with launches from British SSBNs, with three occurring when launched from Ohio class SSBNs. Two of three occurred in 1989, with the last failure occurring in 2011.
It should be noted that British submarines test fire SLBMs at an extremely low rate compared to the US Navy; the US Navy has test fired 4-5 per year since 2012 while Britain has conducted a total of 12 test launches since 1994 (!).
Modernization upgrades don't occur due to poor existing maintenance practices, but to improve the quality of a system so that it does not become poorly maintained in the future. Would you say that the Sovremenny class DDG Taizhou operated by the PLAN is undergoing modernization because it is poorly maintained? It was spotted in drydock on satellite imagery just a couple weeks ago. It is not being upgraded because it is poorly maintained, but to improve the system so that in 5-10 years it will still be effective.
I will note that China also uses modernized versions of very old ICBMs. The DF-5 was first launched in the 1970s, and yet a new variant, the DF-5C, is due to enter service soon (it may have already entered service). The upgrade the Minuteman III underwent in the early 2010s involved replacing virtually every component of the missile apart from the spaceframe. Despite having a first flight decades ago, even old missiles can be upgraded for continued use in the present day.
Scandals involving individuals are not a measure of the combat proficiency of an entire force. PLA commanders have been investigated for discipline violations as recently as this year, but it is not a reflection of the overall capability of the PLA in a war.
The US has always maintained the capability to quickly upload MIRVs to its missiles. This is why many Minuteman III tests are conducted with multiple RVs.
What does nuclear parity with the US achieve that minimum deterrence, upgraded for "comprehensive countervalue" targeting, does not achieve?
It is important to remember that the concept of reaching nuclear parity with an adversary originates in the Soviet Union, which pursued nuclear parity for the express purpose of preventing any conflict in Europe.
In my opinion, the concept of parity is not applicable to China's situation, where it indeed will initiate conflict in Asia (armed reunification of China) within the next two decades or so, assuming the Taiwanese government does not somehow make the decision to peacefully reunite with China.