The Veil isn't a problem. It keeps the Fade and the real world separated. While a mage can tear it or weaken it so can an over abundance of mundane death and destruction. And here's a kick in the pants for you: if the Veil can tear without the aid of magic, but we don't know of a mundane way to repair it and all mages were destroyed; who is going to close it again?
Mages are a potential. They are a potential benefit. They can heal and create.... They are also only a potential problem. They aren't automatically a problem because they're mages. They have abilities that others don't and like with anything, it can be misused. The vagaries of man would still exist, with or without mages. A power hungry man who happens to have a large army under his command or a power hungry man who happens to have magic can both do considerable damage. Most mages don't welcome possession as a matter of course. Most of those examples are seen to occur in desperate situations, like with Thrask's daughter. You back anyone into a corner and they will fight dirty, mage or not.
Magic is only a problem because it is abused at times, which is what I believe Andraste meant when she said it should serve man and not rule over him. As for the Blights? We have the Chantry's word that it was caused by mages. Like with any ancient, unverifiable allegory, I question it's voracity because history is written by the victors after all and among the victors there will always be those who seek to serve their own cause by any means necessary.
I feel magic should be treated with respect. Mages should be educated and there should be some kind of checks system for them. Gun owners have to have a license to legally carry. Yes, I know mages don't choose to have magic but it is still a potential weapon. I don't agree that they should be wiped out or locked up. They aren't criminals just because they were born having magic. They deserve to live and to have the right to self determination like regular people. Most of the worst examples of mages-gone-abomination are as a result of the oppression and abuse they suffer. Any person, mage or not, would become the most vicious of animals if denied freedom, the right to pursue happiness, abused and threatened with death and/or a fate worse than death. Getting rid of mages would be like me taking away all the toys my kids bicker over rather than teaching them to share. It's the easy way out and disservices everyone because there will always be mages born every day. Learning to co-exist and finding a compromise is the only lasting solution I see.