It's true that there was an indecent amount of company rivalry involved in the TSR2 story and the first flight saga was a classic example. It was pretty obvious that the aircraft should have gone to Warton from the start but Vickers clearly thought that the aircraft was their project - and the way that the Government acted simply reinforced this notion. It was Vickers' pre-occupation with VC10 and BAC-111 which encouraged the project to be gradually exported to Warton.
As for whether we needed TSR2 it's back to politics. If we'd remained East of Suez then we obviously would have needed it, but for the European theatre the aircraft was perhaps over-specified. But as has been said, TSR2 eventually led to Tornado which was (for once) the right aircraft for the right role.
I guess one could conclude that no aircraft could be too good and it would have been great if the RAF had received an aircraft which was actually over-specified for the roles to which it was assigned. But everything comes at a price and nobody can doubt that we simply couldn't afford TSR2. Likewise, we can never know just how good TSR2 really would have been. On paper it promised to be a brilliant aircraft but as the flight test programme was hardly even started, and the avionics were still in their infancy, we will never know for sure.