The PLA's paratroop unit is the 15th Airborne Army, which is similar to our 82nd Airborne Division except that they don't jump very often, they don't have much equipment or training, and they don't have much aircraft to move them around.
Putting paratroopers in slow moving aircraft and flying them direcly over the target isn't done anymore. The transport bird will get shot down by either Taiwanese fighters or SAMs, and the PLAAF will lose both the troops and the aircraft.
How many Chinese troops would it take to overrun Taiwan?
There is no land bridge to Taiwan. There are only a few beaches suitable for making a landing, the rest are rocky cliffs. That means that all invading forces must pass through a narrow little corridor before making it in, and to even get to that corridor, they have to traverse 200 odd miles of denied ocean. If the PLAN and PLAAF lose control of the sea while their troops are floating around, Taiwan can smash the bulk of the invasion force while they paddle for shore.
We ain't talking about South Korea here.
No, the Chinese can and have walked to South Korea. They can't walk to Taiwan.
Are you sure our government would attempt to stop a Chinese assault on the Island?
Yes. It would be easy to do, and against the interests of the entire region not to.