My experience is that people in IT abdicate their power and authority. Many of the problems faced by IT are as a result of this.
Some of the things for which IT people ask permission are the equivalent of a garage mechanic asking your permission to reconnect the brakes of your car after a service.
Having the time to experiment with and learn new techniques is vitally important. You won't get that if you are always on the back foot and in fire fighting mode. I find that a refusal from management is rarely a hard NO, it is usually couched in terms that can be interpreted as no and usually an IT person will give up at this point.
In other words, put together a business plan for the introduction of unit tests. It helps if quantifying the problem of NOT having unit tests clearly places your bosses or your bosses bosses initiatives at risk.
Be honest but not too honest. There was a standing joke that if Atari sold KFC they would sell it as warm dead bird.