I think one of the hardest parts of being a photographer is having to connect with complete strangers in very short amounts of time. Sure, some people are easier to talk with than others, but it can definitely be challenge to gain the trust and attention of someone while also guiding them towards what I am trying to accomplish with a photo. When I shoot someones portrait, I like to get them as involved in the creative (and sometimes technical) process as they are interested in. It helps them feel like they are partnering with me towards achieving a goal, rather than just being directed towards an end result they may envision differently than I. When the subject feels like they are part of the process, they often bring ideas up that I may not have thought of that make the image that much better. Collaboration is almost always better than a single persons vision, so why not include the person you're photographing?
I wouldn't at all claim to be a street photographer, but that said, I don't shy away from asking to take a portrait of someone I find interesting. Its a great way to keep exercising my communication skills on the fly in random situations, while trying to develop a story and get a good photo. I grabbed this one while on the 5th Ave bus in NYC a couple years ago, and its one of my favorites. Ask people to be a part of your creative process, see what you learn, and how your work improve because of it.