Yes, travel insurance is worth carrying for a trip through Taoyuan International Airport into Taiwan, though the honest reason has more to do with cost than danger. Taiwan runs a genuinely excellent healthcare system, with modern hospitals in Taipei just a short ride from the airport, but that quality is built around a national insurance scheme that does not automatically extend to foreign visitors, who typically pay out of pocket for treatment. A policy that actually settles hospital bills, rather than one that only reimburses later, matters more here than in many lower-standard destinations.
Typhoon season affects Taiwan roughly June through October, occasionally disrupting flights at Taoyuan and closing roads across the island with little warning; trip-delay cover is worth checking closely if your dates fall within this window. Taiwan also sits in a seismically active zone, and earthquakes are a genuine occasional risk - the island's east coast, including areas around Hualien, has experienced damaging quakes in recent years. Neither risk is a reason for alarm, but a policy that treats natural-disaster disruption as a standard delay claim, rather than an exclusion, is worth confirming before you travel.
Check whether your existing health cover, whether a national scheme, employer plan, or credit-card benefit, extends abroad and specifically to Taiwan before assuming it applies - many stop at the border, and Taiwan's high-quality private facilities do not come cheap for anyone paying independently. A standalone travel policy that pays hospitals directly, or reimburses promptly, is generally the more reliable route for most visitors regardless of what a home plan might technically include.
Keep hospital invoices, prescription receipts, and any airline documentation for typhoon-related delays, since Taiwanese providers and carriers generally issue standard paperwork on request. Many policies also want notice before non-emergency treatment is booked, so check the claims process in your policy wording before you travel rather than assuming automatic reimbursement once you are home.