Your assessment is not entirely correct. There are many examples of magic in fantasy providing social consequences and at least two in the Dresden Files.
The simplest example is intimidation. It is a social attack which you can do either directly with an illusion (to appear more terrifying than you are) or by using magic creatively; Harry uses his "ball of sunshine" spell not as a direct attack on Molly but as an intimidation to test her focus under pressure.
A second, more complicated example is to apply an illusion on somebody else. You can make them look different and, if made to look somehow repulsive, you can divest them of their social advantages both because their contacts and resources won't recognise them and because they'll be, well, repulsive. Making someone's clothes look soiled, making them look old and ill or applying to them a certain repulsive odor or weird sounds when they move is certainly a possibility. A certain evil witch does that to Harry's brother and Harry, failing to recognize Thomas, ends up attacking him.
A third example is a social veil; instead of making them invisible, make their actions and words seem insignificant; when they try to influence others socially, said others will ignore them. When they try to use their contacts, their contacts will overlook them. When they try to speak their mind, their words will be ignored. Bonus points if instead of making all their attempts blocked, make only their attempts regarding a specific subject seem overboard or unreasonable. And then you use your own social skills to convince everybody else they are grief-stricken, insane, full of rage or whatever and that they should be locked up.
Last but not least, there is nothing more embarassing than making someone's clothes invisible in public... while also having the illusion apply subtle faults to their physique.
