How important is it to let a stranger finish his sentences?
- Professional environment: VERY important / mandatory
-> you don't stop your boss/manager/co-worker/client from talking/explaining his point of view. Not doing so is not only totally unprofessional, it's also definitely rude.
- Personal/friendly environment: VERY important for many Westerners -> in western culture, it's much more than in other parts of the world, according to Professor Tannen - Linguistics Department - Georgetown University in a 1992 New York Times article:
"The two forms of completing another's sentence are interruption and overlap ," she explained. "Either you may interrupt the other person, as in taking advantage of a pause, or you may chime in, in chorus with the other speaker."
Professor Tannen calls this type of conversation "high-involvement style," which includes standing close, talking loudly and leaping from topic to topic. Cultures that feature this style include Eastern Europeans, Mediterraneans, Africans and Arabs; women, Professor Tannen reports, finish others' sentences more often than men do.
Would one be annoyed or glad he got an answer to his question quickly?
- Professional environment: if it happens on a regular basis, no matter if you actually answered his/her question, the person will see the naysayer as unprofessional and rude. If it happens once in a while, you may just apologize: "I'm sorry for interrupting, please go ahead".
- Personal/friendly environment: you already answered your own question, saying your friends/family are now used to that. But letting go and not saying anything doesn't mean agreeing...
Is it considered impolite?
Under most circumstances: YES.
Is it tolerated for the sake of effectiveness in our western society?
I can't say for so many different countries and culture, but from what you said of yourself, you seem to give people only the choice for tolerating it. Even if you're smart (er than others), don't be condescending. Maybe it's time for a Talking Stick :)
Looking for sources and references, I came across ADHD : Attention Deficit Hyperactivity Disorder. If you want to read about it, some points are really interesting and may show you workarounds, even if it's not a disorder you suffer from. Symptoms include :
- Inattention (lack focus and listening)
- Hyperactivity (always be "on the go")
- Impulsivity / Impatience (having a hard time waiting to talk or react)
Other links: Adults ADHD and Stop finishing other people's sentences
NOTE: being a kid/teenager, I often did that to people to draw attention, and it bothered me as much as it bothered them. I found 2 tricks: 1. count mentally to seven before answering/asking 2. in class, put my thumb and middle finger under my chin, with my index on my mouth. That was a great self-taught "S*** U*" :)