Yes, travel insurance is worth carrying through Tokyo Haneda, though the honest reason has more to do with cost than any real danger. Japan has some of the most modern, well-run hospital care anywhere in the world, and Haneda, built on reclaimed land in Tokyo Bay just south of the city center, puts you within easy reach of it from the moment you land. The catch is that this level of care is not free for visitors without local coverage, and unlike some countries, Japanese clinics and hospitals commonly expect payment at the time of treatment rather than billing an insurer directly.
Because the quality of care is not in question, the real work for a policy here is smoothing out the payment gap: look for coverage that reimburses promptly and without excessive documentation, since you may need to pay upfront yourself before any claim is processed. This is a cost and cash-flow issue far more than a facility-quality one, and it is worth planning for rather than assuming a policy alone prevents an out-of-pocket bill.
Japan sits on some of the most seismically active ground on earth, and earthquakes are a genuine, routine feature of life here rather than a remote possibility; the country's early-warning alerts reach phones seconds before shaking starts, and most travelers experience at most a minor tremor without incident. Typhoon season, roughly June through October with a peak in August and September, is the more disruptive risk for a Haneda itinerary, regularly delaying or cancelling flights with real but limited notice. Confirm your policy covers weather-related trip delay specifically, since a typhoon grounding flights at Haneda is a fairly routine seasonal event.
Keep hospital invoices and payment receipts for any treatment, since Japanese providers issue detailed paperwork that most insurers accept without much back-and-forth. Confirm whether your policy reimburses you after you pay or settles directly with the provider, and check the claims-reporting window in the wording before you travel, since Haneda's typhoon-season disruption is the more likely reason you will actually file a claim.