Why weren't the Airbus A330 engines designed with a system to stop their fans?
Complexity and weight, what airlines hate most.

Has it been done before? Yup. A variant of the Convair B-36 Peacemaker was able to stop the windmilling when the jet engines were not needed (that variant had 6 piston engines and 4 jet engines).

(Source)


  The metal petals filling the inlet prevented the jets from turning in the wind as the B-36 cruised for long periods of time with them turned off. The petals retracted to allow the jet engines to be ignited for extra thrust during take-off and high speed dashes. A strut braces the nacelle against swinging from side-to-side.


Scaling this up for the big diameter engines for that very rare engine failure is not cost effective. Instead planes can survive, and are extensively tested for, vibration and flutter.

How rare is very rare?


  By the 1970s, advancing technology had set the stage for two-engine, turbine-powered airplanes to safely exceed the 60-min operating restriction [away from the nearest airport]. The result was ETOPS, which began in 1985 with 120-min diversion authority and the requirement for an average engine in-flight shutdown (IFSD) rate of just 0.05 per 1,000 engine-hours. With 180-min ETOPS authority, which followed in 1988, an even more stringent reliability target of just 0.02 IFSDs per 1,000 engine-hours was specified (Boeing, 2003).