>do you really get work done in a coffee shop or any kind of public place like that?
Yes, definitely.
For me it's that despite the noise, I have complete confidence that none of it is relevant to me, so I can ignore it completely. In offices, tons of things are relevant for me because I'm a popular random-problem-solver. At home, anything could be relevant, even though most of it is not.
The noise isn't the issue, it's the brainpower spent on triaging the noise.