The United States has been arbiter of the Taiwan Strait since the final retreat from the Chinese mainland of the Guomindang (KMT or GMD). It was not until 1971 that the United States even recognized the Communist government in Beijing as the government of China (previously, the KMT government on Taiwan was recognized as government of the entire country).
To be short, we've come a long way since then. And I believe the last decade marked what was, ultimately, the end of inter-Strait tensions as we know it. And the US has had a major hand in that.
For Taiwan to ease up to China, a few things had to happen. One was obviously the rather overwhelming economic benefits of opening up to the Mainland. But the United States had to carefully wean Taiwan off its own dependence into an economic autonomy that drove it towards China.
Similarly, the United States had to slowly decrease its military support for Taiwan, balancing a need to not scare the Taiwanese into believing they were abandoned military. And, surely, they have not been. The United States would still respond militarily to Mainland aggression across the Strait, that is clear. But the fact that Taiwan is becoming a decreasingly effective regional power has helped to assure the Mainland of its position as arbiter of all of China, whether in name or not.
Cross-strait integration may not seem like a major positive, but it is, and it has been executed well. Taiwan has moved towards the Mainland of its own accord, giving no diplomatic or political bending on the part of the United States in its stance towards China in general. The US remained firm on key issues with respect to China, including trade, human rights, spying, etc. And certainly, there is no doubt that Beijing has done little to please Washington, but I intend to drive the following point: relations with China could have been very poor, and could have dominated much of US foreign policy.
The defusing of the Taiwan strait tensions--probably for good--have led to a rather dramatic decline in hype over the Chinese military. Taiwan as a strategic stronghold for US naval power proved to be more a liability than an asset by the 2000s, and the gradual nudging towards the Mainland that the US encouraged proved a very long and elegant diplomatic maneuver that has saved, and will save, many headaches into the future as the US continues to deal with Russia and the Middle East as primary strategic threats.