Vienna rarely tops any list of risky destinations, and that is largely true - but the honest reason to still carry travel insurance here is what many visitors do before or after the city: time in the Austrian Alps, or a river cruise departing along the Danube. The capital itself poses little unusual risk, and a policy built purely around a city stay usually undersells what the rest of the trip needs.
If skiing or other winter sports feature anywhere in the itinerary - Tyrol, Salzburgerland, or another Alpine region reached from Vienna - check that your policy names winter sports specifically rather than assuming a standard city-break policy extends automatically to the slopes. Off-piste skiing and higher-altitude routes are commonly treated differently from ordinary resort skiing in policy wording, so confirm any exclusions before you leave the capital. Danube river cruises departing Vienna toward Budapest or Bratislava carry their own trip-disruption profile too, since a missed sailing or a port-schedule change is a more common claim than any onboard medical issue.
For the city portion of the trip, the real question is not danger but whether your own cover reaches Austria at all. Check whether your existing health cover, including any EHIC, GHIC, or national-scheme arrangement, extends abroad and specifically to Austria before assuming it applies, and treat any such arrangement as a supplement to, not a replacement for, standalone travel insurance.
Keep any clinic invoices from Vienna and, if your trip includes an Alpine leg or a river cruise, resort, rescue, or cruise-line paperwork as well, since claims involving mountain activity or a missed sailing generally need more documentation than routine city treatment. Many policies also require notice before non-emergency treatment or evacuation is arranged, so confirm the process before combining a Vienna stay with either the Alps or a Danube itinerary.