You're right, as an exhibition piece it would had been quite an attraction. But it was not up to the Bristol company to decide her fate.
During and after the war, most British aviation development was managed by the government. The Brabazon was the result of a committee which set the goal to develop a transatlantic airliner with 1943 technology, not by a company and its technological visionaries. If you had asked people like Willy Messerschmitt in 1943 how the future airliner would look like, he would had basically described a Boeing 707: Swept wings, turbojet engines, pressurized cabin for about 100 passengers. But Government bureaucrats put the goal for the Brabazon quite differently, and the result was technically obsolete by the time it took to the air. Even before the Brabazon flew first on September 4, 1949, the de Havilland Comet had already flown on July 27, 1949 and was on its way to revolutionize air travel. Its development had started later and was directed by engineers, not bureaucrats.
When that became obvious, the bureaucracy felt too embarrassed to keep the Brabazon around. The situation was similar to Beechcraft and the Starship: Burt Rutan's 85% scale prototype was cut into pieces out of spite when it became eventually clear even for Beechcraft's board just what a turkey it was. The same fate befell the Brabazon.
But its legacy for Bristol is still very positive - without the Brabazon, it would certainly not employ as many people in aerospace as it does up to this day.