Yes, travel insurance is worth carrying for a trip to Amsterdam, and the most distinctive reason has nothing to do with the canals or museums - it is the bicycle traffic. Amsterdam's cycling infrastructure is genuinely extensive, and visitors unfamiliar with the dedicated bike lanes threading through the city are a common source of minor and occasionally serious injury, whether on a rented bike or simply stepping into a lane while looking the wrong way. The Netherlands otherwise has excellent, well-organized hospital care, so this is a real but manageable risk rather than a dramatic one.
Whether your own health cover applies here depends on your country of residence and plan: EU citizens with a valid EHIC and UK travelers with a GHIC card can access Dutch public healthcare on terms similar to residents, but this is not a substitute for a full travel policy covering repatriation or care outside that system entirely. Check whether your existing cover extends to the Netherlands specifically before relying on an EHIC or GHIC alone, since neither covers everything a travel policy typically does.
Cycling is the activity risk worth naming specifically here - renting a bike to explore the city is one of the most common things a visitor does in Amsterdam, and a fall or collision in traffic is a realistic, everyday scenario rather than a remote possibility. Confirm your policy covers cycling-related injury and, if you plan to cycle further afield into the surrounding countryside, that it treats recreational cycling as ordinary activity rather than an excluded sport.
Keep any clinic or hospital paperwork, police reports for a traffic incident, and receipts for treatment or bike repair if something goes wrong, since claims involving a cycling accident benefit from clear documentation of how it happened. Many policies also want prompt notice before non-emergency treatment is booked, so check the claims process in your policy wording before you travel rather than after an incident on a busy Amsterdam bike lane.