Mild spoilers for Daredevil Season 2 are below.
As Nelson and Murdock’s “legal assistant who is seen doing more work than her bosses most of the time,” Karen Page is often portrayed as intelligent and adept at research, if a little unformed where emotional responses are in play. There are many viewers that think Karen’s lack of ignorance should make her far more cognizant of the blatant connection between Matt and the Man Without Fear, but actress Deborah Ann Woll has a perfectly good reason for why it’s okay for Karen to still be in the dark on Matt’s secret life.
I believe she wouldn’t connect them because I’m actually experiencing this and there’s not enough evidence yet for me to connect them.
What she’s saying here is that Karen has only come into contact with Daredevil on very few occasions, and they weren’t exactly the sort of interactions allowing time for her to sit down and study the costumed vigilante beneath a high-wattage light bulb. And when they first connected, she barely knew who Matt was in the first place, so there definitely wouldn’t have been any reason to jump to that conclusion then. Even though she’s getting closer to Matt in Season 2, that doesn’t necessarily mean that she’s also getting closer to Daredevil (even if it does actually mean that).
As well, no sane person would automatically assume that one of their closest friends or co-workers is the guy going around at night and putting his life on the line trying to stop all of the crime in the area. Especially when the guy is blind and not exactly the most aggressive person in public. Also, she probably wouldn’t think that someone as cool as Daredevil would be friends with Foggy, which is kind of half-right, considering how often Foggy likes to take friendship hiatuses.
The show even kind of sets it up for Karen to take Matt's lacking worth ethic and lack of dependability on going out and getting wasted and messing up his life. And her displeasure with him on certain fronts certainly doesn't make her more likely to guess that he's responsible for all the headline news in Hell's Kitchen.
Deborah Ann Woll also told IGN why her own habits as an actress keep her from thinking of Matt and his hero side as the same person.
I have a policy for a lot of different reasons that I don't actually watch the work that I do. There's all kinds of reasons to do that, but one really interesting side effect that has come about from that is that I have no imagery of the show that isn't from first-person, that isn't through Karen's eyes. What that means is that every time, as Karen, I encounter Daredevil or think about him or anything, he's like a ghost. He's like this exceptional being that I have no concrete sense of -- and I like that.
Hell, Superman himself Henry Cavill put recognition of a superhero to a test recently and discovered that people don’t always recognize things even when they’re in plain sight. I’m sure most people are still saying, “Yeah, but not me. I would definitely recognize him.”
People like Frank Castle and Luke Cage don’t need to wear a mask when they’re out in the city getting their crimestopper on. So if Karen ever finds herself not recognizing them from one situation to the next, that's on her.