After the Night of a Thousand Arcane Duels in 2415, the Church of Sigmar pressured Dieter IV to close the Colleges and ban magic. As Dieter IV never heard a bad idea he didn't love, he went along with it. Ironically, this healed most of the leftover rifts from the Night because all eight College basically closed ranks and said "come and have a go if you think you're hard enough", and though many Witch Hunters believed they were hard enough, all of them turned out to be incorrect. Most of the esoteric and paranoid defences of the Colleges date back to this period. In 2420, Dieter IV managed to completely tank any goodwill he got from banning the Colleges when he accepted a bribe to sanction a College of Elementalists in Nuln.
In 2429, Dieter IV was deposed after accepting a massive bribe to grant Marienburg independence. Emperor Wilhelm III, also known as Wilhelm the Wise (mostly out of contrast) and the current Emperor's grandfather, got off to a bad start when some circus illusionists made off with a significant chunk of his treasury and he tried to hold a mass trial for wizardry in general on charges of 'witchcraft and consorting with Chaos'. The Colleges were into year fourteen of their 'siege' at this point, so funnily enough none of them arrived to defend themselves. The trial was postponed for Wilhelm III to go reconquer Marienburg, but they were allied with Ulthuan and things went devastatingly bad for the forces of the Empire. Wilhelm went 'wow okay point fucking made holy shit' and reopened the Colleges in 2430.
Official history records the Great Fire of Altdorf that burned the district surrounding the Bright College as happening in 2431, as part of an 'accident' when 'rebuilding' the College. It's probably for the best if you pretend to believe that.
The College of Elementalism still exists as a branch of the University of Nuln under extremely close scrutiny from both the Templars and the Colleges. It lacks the prestige and the power of the Colleges, but it still attracts students. Apprentices that don't want to live with the obligations of the Teclisean Colleges but don't want their magic suppressed either often end up 'running away' to Nuln, and as they still technically exist under an Emperor-recognized College of Magic they're legally in the clear. The Colleges usually consider getting rid of someone with the belief of 'I want power but I don't want to actually help the Empire with it' to be in their best interest, and them going to Nuln means at least they're not learning necromancy or sorcery, and they're easy to keep an eye on.
Do not meddle in the affairs of wizards, because 'subtle' and 'quick to anger' still only covers two of the eight terrifying flavours they come in.