Good points, though in The Deadly Assassin the TARDIS is referred to by Gallifreyans such as Castellan Spandrell as "a type 40 TT capsule". Maybe the name caught on with the general Gallifreyan public and only retained its technical classification with specialists and similar?
At the age of five, Skagra decided emphatically that God did not exist. This revelation tends to make most people in the universe who have it react in one of two ways - with relief or with despair. Only Skagra responded to it by thinking, 'Wait a second. That means there's a situation vacant.'