I don't know if magic would be impossible to hide from mortals; I suppose it depends on the ratio of wizards to mortals in the world population.
Of course, the Wizard World leadership makes exceptions: Alex is the Russo family wizard, but Justin's powers were restored when Professor Crumbs named him to lead Wiz Tech. (Maybe there's an obscure technicality that would allow Max to get his powers again, but I think he's happy as a mortal.)
Yeah, I know filankey is not a word, but it's gonna catch on.
Max was definitely meant to be mortal, because he hardly ever used magic anyway. He was the same old Max in The Wizards Return, and it didn't occur to me that his wizard powers were gone until several days after I was finished watching it.
"Does your society have any other adjectives besides 'great'?" - Pvt. Church
I think it's an un-renewable resource analogy. There have been several mentions to magic being like electricity: the Wizard fuse box, a Generator, rolling blackouts. So too many Wizards drains the source of magic energy. So Crumbs retiring means he can give his power to Justin.
I think there's a number of reasons. One of them being the one you mentioned, another being the thing the other person mentioned about the balance of magical power, I think also because it gives the young wizards a reason to really learn magic. School is boring, most things we forget after we take the quiz. The wizard world can't afford to have a bunch of lazy wizards. Some will put in the effort to really learn magic but most probably would not... unless they had to.