The one fixed outfit thing was only actually a thing in the 1980s. Hartnell didn't vary much, but his hat and monocle weren't worn all the time. Troughton's Doctor initially would use disguises often, and was also a hat fan. Pertwee as already mentioned had different jackets and his cravat wasn't always present. Tom Baker has several different outfits, used according to the story genre. The fixed uniform thing started in his last season, when he always wore burgundy. Peter Davison and Colin Baker almost always wore their cricket outfit and multicoloured jacket, though Colin did switch the jacket for a waistcoat in The Two Doctors, which was filmed abroad in very hot temperatures. Sylvester McCoy had two slightly different outfits in his initial three years on screen, then changed his outfit completely at some point prior to the 1996 TV movie. Eccleston had several different colours of jumper underneath that leather jacket, Tennant had three different suits (pinstripe, blue, and tuxedo), Matt Smith had four different regular outfits (tweed, green jacket, a different tweed, and his final purple one).
The show has actually referenced this a few times. Rose dressed up in period appropriate attire for The Unquiet Dead. The Doctor didn't: "I changed my jumper!" Later, both Rose and the Doctor got called out in The Doctor Dances, for wearing a flag and a U-boat captain's jacket during World War II!