It does. You can take the red lyrium away from a templar before he goes crazy, but you can't take the magic out of a mage.
Well, you can. But that involves tranquillity. Which is one of the things mages rebelled over in the first place.
If we could just 'take it away', the reds wouldn't be a major faction/antagonist in Inquisition. Which makes them ticking time bombs. There's also the lyrium addiction which can be manipulated by certain factions to radically alter Templar behavior.
There are also the Templars who are monstrously abusive (Karras) or end up losing their minds (Meredith). And then there are mages like Bethany and Malcolm, who are pretty much heroes without a blemish on their records.
Also, Tranquility is one of the things some mages rebelled over; there are numerous perspectives about tranquility in the mage community.
The point being that these sweeping statements about mages being ticking time bombs couldn't be more false; it all depends on the individual for both mages and templars.
Absolutist bs like that is what got us in this predicament in the first place.