Yes, travel insurance is worth carrying for a trip through Sydney, and the case here rests more on cost and onward plans than on any unusual danger in the city itself. Australia has excellent, modern hospital care, and Sydney's own facilities are as good as any in the country, but that care is not automatically free for every visitor - reciprocal healthcare arrangements exist with only some countries, and coverage for everyone else depends entirely on the traveler's own arrangements.
Whether your home country has a reciprocal healthcare agreement with Australia, and what it actually covers, varies enough that this page cannot answer it for you; check your own government's guidance and your existing health cover before assuming either applies, and treat a standalone travel policy as the more reliable baseline regardless. Sydney itself poses little unusual medical risk beyond normal urban travel.
Many visitors use Sydney as the gateway for onward trips into the outback or up to the Great Barrier Reef further north, and both bring a genuinely different risk profile than the city - remote distances, limited phone signal and services inland, and diving or snorkeling exposure on the reef. Confirm your policy names remote or outback travel and diving specifically if either is part of your itinerary, since a city-focused policy sometimes underinsures both.
Bushfire season, broadly the Australian summer from roughly November through February, occasionally affects travel and air quality around New South Wales and can disrupt regional flights; check that your policy covers weather or bushfire-related trip delay if your dates fall in this window. Keep any hospital invoices, prescription receipts, and airline documentation for delays, since Australian providers generally issue standard paperwork on request, and confirm whether your policy pays facilities directly or requires you to pay first and claim afterward, particularly if your onward plans reach far beyond the city itself.