I'm the opposite, I liked her at first and over time I started hating her.
Her position in the inquisition didn't seem entirely OOC to me, since she does have connection to the Friends of Red Jenny's, who can act as an additional spy network for the inquisition. As shown during her recruitment mission, she led you to a guy who was pretty much like, "So, Herald you discovered my evil plot to undermine the inquisition." Despite us never getting a chance to really interrogate him, he made it clear enough to me that he was an enemy of the organization.
Even though her explanation of how the Friends work doesn't make them sound very useful on the surface, but if you look deeper at it. The Friends are made up of servants and the lower class, people who work in close contact with nobility. Nobility who think that they don't have to worry about the inferior underclass, so they are much less careful around them enough that they might blab about their hostilities towards you when their servants are around. These servants then might give a tip to Sera about this and then she will tell you so that you can effectively deal with this potential threat.
Why an inquisitor would want to spend time with her at the start, falls mostly on who your quizz is. My first quizz felt stressed out and overwhelmed by her new title and position. So playing around with Sera got her mind off of it and gave her chance to go back to being just a person. Also, Sera sees the quizz more as a person from the get go, unlike many of the other companions, such as Varric who says to you that he sometimes forget that you aren't like those statues of Andraste holding bowls of fire. Being seen as a religious symbol can be very difficult for someone to deal with and having Sera see past that can be very refreshing.
That being said, I still don't like her. Her abrasiveness personality and b***ness towards my elf quizz made me dislike her.