Because they can't.
1) Taiwan is a VERY big island. One thing about America is we often see foreign countries on large-scale world maps and don't get a sense of just how BIG some places are that look small on maps.
2) The Taiwanese Army has more troops, and is FAR better armed, than the German forces defending Nortwestern France in WWII.
3) Taiwan has very few good landing beaches, fewer than France did, and weather in the Taiwan Strait is often bad. And the Taiwan Strait is over twice as wide as the English Channel.
4) A large scale amphibious landing against defended beaches is the most difficult thing to do of ANYTHING, militarily. The US and Britain have done it a lot from WWII to today, giving the impression it's easy. It required huge amounts of practice and planning, and gradual buildup to larger and larger invasions.
5) A successful invasion and conquest of Taiwan would likely require the largest invasion force ever mounted..larger than Normandy, larger than the US invasion of Leyte and Luzon in WWII.
6) The Chinese have NEVER mounted an amphibious invasion of ANYWHERE in modern military history.
7) The Chinese miltary is one of the most completely inexperienced in the world. Last major war was Korea, and pretty much everyone with experience in that war is dead or long retired. Other than brief border clashes with the Soviets in the late 1960s, the (successful) war with India in the early 1960s, and the brief invasion of Vietnam in 1979 (where the Vietnamese really kicked the crap out of them) the Chinese military is totally inexperienced. Basically no military operations of any kind for 20 years. And many of their generals have been more busy running factories than training troops.
8) The United States has BY FAR the largest amphibious shipping capacity in the world...and if we got ALL of what we have, we could MAYBE land one division of troops simultaneously...about 15,000-20,000 guys. WE woudn't have enough amphib shipping to invade Taiwan. China has a TINY fraction of our shipping. People have come up with Rube Goldberg theories about having Container ships secretly filled with troops enter Taiwanese ports, etc, but you not only have to get troops ashore, you've got to keep them SUPPLIED afterwards.
9)You need COMPLETE air supremacy over the beaches for an invasion to succeed. The PRC air force, while large on paper, is overwhelmingly comprised of VERY obsolete aircraft, and there isn't room to base most of them in range of Taiwan, anyway. The Taiwanese have a reasonable number of modern fighter aircraft, and they'll be on the defense, giving them an advantage. I'm dubious the PRC can get air supremacy, even WITHOUT US aid. Even ONE US Carrier makes it COMPLETELY hopeless for the PRC in the air.
10) The PRC Navy is really a pretty sad force. Most of their subs are inoperable, most of the surface vessels are small and obsolete. Their few nuc subs leak radiation and are VERY noisy. VERY few modern forces and most of the hype stuff you hear about are ex-Russian carriers that will never see service again, and stuff the Chinese have paid the Russians to build them but that hasn't entered service yet.
11) A failed invasion likely means the collapse of the PRC government completely, as was the case with Argentina and its military junta and the Falklands...they can't survive the loss of face. They wouldn't try it unless they were SURE of success, and realistically they have about a .001% chance of success. That's why they haven't done it...they can't.
Militarily, there are only two options. Come into the beaches or parachute in, take the airports, and then bring im large troop planes. Only about 15% of Taiwan's shoreline is capable of sea launched assault. And you'd better believe that is well defended. Same goes for the Taiwan airports which are large enough to land large troop planes and are also heavily defended.
Last possible option is gluiders, which could land anywhere. (Recall A Bridge Too Far.) China doesn't have the gliders, but even if they did, it's technically much harder to cross the Striats of Taiwan, than the English Channel.
Bottom line: China cannot take Taiwan now. I assume, however, that they have plans and developments in the works so they could take it in a few years. In the meantime, they have already positioned medium-range missiles on the coast so they could give Taiwan a hell of a pounding that way, without an invasion.
Congressman Billybob
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