In The Professional you need to justify the emotional connection between Leon and Mathilda because Mathilda is a stranger who waltzes into his apartment one morning and, before then, they were strangers to each other. And that is the emotional crux upon which the whole narrative spins.
In The Bourne Identity, a connection is formed between Jason and Marie as they share this emotional experience together and it blooms into romance. This is a standard in spy thrillers (the romance between hero and heroine) and it gives the back story necessary to justify the drive of Supremacy...
But in Taken... She's his daughter. In a 100 minute movie, meant to be a basic roller-coaster, that is more concerned with action beats and plot momentum than anything else - wasting time with establishing an unnecessary justification would only bog it down. The movie is not about why they are connected. That's self-explanatory.
Being a parent, I didn't need to know why Neeson wanted to find his daughter. That he's been an absentee father most of her life is irrelevant. It doesn't mean he doesn't love her. In fact, the one flaw I did find in the film is that it took too long to get moving precisely because they had to establish all this back story about the divorce and his controlling relationship with his daughter and it makes the first 20-odd minutes kind of slow. He's her dad. Some creeps have kidnapped her. That's all you need to know.
Why does he care? Because he's her father. End of story.
