Admiral Fisher argued that the role of normal cruisers would be better served by a ship that was larger and more heavily armed, but faster. "Speed is protection" and all.
Was there any circumstances in which the battlecruiser worked as intended? As against modern naval weaponry, speed didn't seem to be protection at all. Perhaps they could have been better used as commerce raiders than in actual battles? Or were they a waste of money and material; which could have been better spent on normal cruisers?
The battlecruiser was intended as a cruiser replacement, yes, but they were not intended to replace all cruisers. They were a replacement for the large 'first-class' armoured cruisers, which were primarily built to act with the battlefleet. They operated as heavy scouts, and as a 'fast wing' of the battlefleet. In the former role, they saw significant success at Jutland - despite the losses, the British battlecruisers were able to prevent the German light forces from locating the main body of the Grand Fleet. They also saw significant success against German light forces at the 1st Battle of the Heligoland Bight. The British also detached a number of their battlecruisers to hunt down the German East Asia Squadron, though this was after an armoured cruiser force already deployed to hunt this squadron had been defeated at Coronel. The British battlecruisers won a decisive victory at the Falklands Islands. For more information on battlecruisers, see my previous answer here.