Obviously the actual number of missiles Taiwan has is not public, but I suspect they have enough that reliably intercepting a full barrage is not something even the us could pull off.
The general calculus is that an interceptor costs as much as the missile it intercepts, so defenses are only effective against an adversary with much less resources. Hence Israel can defend against Hamas/Hezbollah, and the US can defend against North Korea, but Israel struggles against Iran and the US doesn't even try to defend against China/Russia.
China obviously has a lot more resources than Taiwan, but then you have a concentration effect where an attacker can focus their resources on a single target, but a much more resourced defender can't necessarily afford to defend that target. We saw that play out with the UK's nuclear deterrent strategy in the cold war, where they focused on overwhelming Moscow's defenses, and were (probably) able to do it despite the USSR being so much bigger.
The general calculus is that an interceptor costs as much as the missile it intercepts, so defenses are only effective against an adversary with much less resources. Hence Israel can defend against Hamas/Hezbollah, and the US can defend against North Korea, but Israel struggles against Iran and the US doesn't even try to defend against China/Russia.
China obviously has a lot more resources than Taiwan, but then you have a concentration effect where an attacker can focus their resources on a single target, but a much more resourced defender can't necessarily afford to defend that target. We saw that play out with the UK's nuclear deterrent strategy in the cold war, where they focused on overwhelming Moscow's defenses, and were (probably) able to do it despite the USSR being so much bigger.