I'm Dr. Jackie, an interpersonal communication researcher/professor and relationship expert. And no, it is not unreasonable at all. Like you, I would want my kids (they are younger, not even teens yet) when they are dating to introduce their bfs and gfs to me and my husband in person. Unfortunately, today's generation is so connected to social media that that honestly is what they know. People become friends, becoming dating partners and yes BREAK UP all through social media. So I think it is not just your daughter or even a matter of being disrespectful, at least not intentionally. I don't know her, so of course, I don't want to speak for her. But as a college professor of many 18-22 year olds, I can hardly get through half a lecture without having to call down students, threaten loss of grade points, etc. for texting or being on FB IN CLASS!!!
I know this is not much of an answer, and I'm willing to try to answer better if you would like, but society unfortunately dictates a lot of people's life styles, life choices, manner of daily living, etc. And today, everything is soooo immediate that we usually find out about it from FB, Twitter, or some other social media. Ironically, the rate of suicide, substance abuse, etc. is steadily rising. I don't know if there is a correlation or not, but I'm guessing that because information is so "in our face" like never before, and we don't even stop to try to process it, we are raising ticking time bombs to some extent.
I am hopeful that if you have a good relationship with your daughter, that you can talk to her about this and remind her that you love her so much and care about her choices and just want to meet someone who is important to her.
I am hoping this helps a little--do you want to write back and forth some more?