Airspace incursions are a more or less legal (definitely closer to the less side) way of forcing an opponent to incur attrition. Just fight hours on planes is extremely expensive and somewhat dangerous. So forcing jets to scramble causes the other side to spend money you might be in a better position to absorb.
ADIZ is not a nation's airspace, which is actually part of it's territory according to international law. In fact ADIZs have zero basis on international law, neither Taiwan's nor China's nor the USA's.
With that in mind it should be no surprise that ADIZs are way bigger than a country's airspace (which matches it's territorial waters). Taiwan's extends over mainland China. Of course they don't report on Chinese planes flying over China but even the median line is way further out than the 12nmi of territorial waters/airspace a country is entitled to.
Of course China also arbitrarily claim to have an ADIZ as well as arbitrarily claiming the whole strait to be internal waters thus their territory.
Taiwan also claim they are the rightful government of the territory of the CPR. Nothing arbitrary, the states are the offspring of two opposing sides in a civil war. For decades Taiwan even kept claiming Mongolia as their territory.