Taiwan has at least 1 anti ship missile for every Chinese vessel and 1 anti air missile for every Chinese aircraft, and this just from US-supplied weaponry(I encourage you to read the Wikipedia article above). Taiwan also has hundreds of domestic missiles that can hit as far as Wuhan, and at least 50(and more coming) that can hit Beijing.

You say Taiwan can't do anything in a war, but this certainly seems like a lot of something. Propaganda or no, things tend to explode when you shoot missiles at them.

That said, certainly China would eventually succeed in invading Taiwan(barring foreign intervention), however China knows the cost of invasion and is not willing to pay it, so Taiwan keeps buying more weapons to ensure the price remains high for China.

Were it not the case, China would have invaded by now.

So instead China is doing slow diplomacy and hoping sentiment in the Taiwanese govt and people trend towards unification.