Hogwarts school of witchraft and wizardry Wizards have a number of useful and powerful abilities with magic. They can summon objects out of existence, multiply them, alter them. They can change their own apperance, make people forget, create new memories and more. Their civil engineering would be highly useful … … and yet. Most wizards only have some of those abilities. The teachers, the ones who demonstrate the abilities to the students, are the creme, in the top 5% of mages by ability overall and certainly well within the top 1% of their chosen speciality. Most wizards can use magic for mundane things, like keeping your house nice and tidy or casting an occasional spell to get around. This is alluded in the fourth book, where Moody tells the children they could cast the killing curse on him all at once and it would only cause him a nosebleed. Their most dangerous ability is the Imperious curse, which could be used to cause havoc in the muggle world. Yet only a small portion of wizards could use one to command an adult. That’s why wizards went into hiding. They fought a war against muggles, lost and the statue of secrecy was born to protect them. That’s why Voldemort is trying to conquer the wizarding world first, a united wizardkind might stand a chance of subjugating the muggle world. A lone wizard with a core of followers can’t hope to achieve anything.