Depends some on how serious your death barrier is. Some worlds treat death like it's no big deal. You're dead, but you can come back when X happens or after enough time has passed. In such worlds, a necromancer becomes a cog in the machine and little more. The problem with this type of world is that death becomes a rather cheap mechanism
In the comic book fan community, the apparent death and subsequent return of a long-running character is often called a comic book death. While death is a serious subject, a comic book death is generally not taken seriously in the real world and is rarely permanent or meaningful other than for story or thematic purposes.
More often, though, death is as serious as it is in the real world. In the real world, the dead don't return. In other words, death becomes a rule. This brings up some flaws they tend to suffer from
#Flaw #1: The high cost of raising the dead
Flaw #1: The high cost of raising the dead
I can think of dozens of stories where the price to break the rule is incredibly high. A common theme is returning a dead person costs the life of someone else (the Naruto universe is one example).
#Flaw #2: The ends justify the means
Flaw #2: The ends justify the means
We tend to view people who break rules very dimly anyways. The problem, as with any story, is that once you break a rule, breaking any other rule becomes steadily easier. Probably the best modern example of this would be Lord Voldemort of the Harry Potter series. He discovers a way to cheat death, but doing so means killing someone to obtain this power. As you learn throughout the series, it involved killing not just people for the power to cheat death, but killing people who didn't like that he was killing people.
#Flaw #3: The product is deeply flawed
Flaw #3: The product is deeply flawed
Necromancy seldom produces something as good as the original. It's like a caricature of the person. Zombies are mindless corpses. Most other stories will typically give you something that is just less than the original. In other words, Necromancy generally cannot satisfy the desires of the person who wants the dead returned.