Abnormally loud exhaust systems reduce the efficiency of the engine and increase fuel consumption . A Porsche 911 doesn't have a loud exhaust system but produces a fair whack of power from its engine.
F1 cars (and any racing car not subject to noise restrictions) have straight through exhausts, in order to get exhaust gases away and out of the engine as soon as possible, thus making the engine more efficent. Fuel consumption isn't a requirement!!! Power is.
fitting a larger diameter exhaust alters the valve timing on the engine by reducing the designed back pressure on the system-therefore in theory the vehicle could actually run worse with a loud system and use more fuel-ideally set the car up on a dynamometer-but that's expensive!