Says the attention deficited introvert in his very quiet house far, far out in the boondocks.
Home is a very bad place for me to try to focus because I'm constantly reminded of things that need to be fixed, painted, washed, etc. And if there are other humans in the home it's even worse because you know I could be socializing with them, helping them with their homework, fixing their computer problems...
So a coffee shop is an improvement because a) Starbucks people are responsible for fixing the plumbing problems and b) I don't know anyone there.
Now that I have a job, I'll often go to coffee shops if I work on the weekend. And, again, it's because doing it by myself, at home, feels very isolating. Even though I like having time to myself late in the evening, it's rare that I want no social interaction during the day. And if I need to get work done during that day, I'll often use a coffee shop.
And oftentimes it's the novelty of a place that helps inspire some creativity when it comes to writing.
As others have pointed out, it's hard to shut out conversation from coworkers especially if you don't know if they are talking about work related to you. But when you're in public, you know those conversations don't pertain to you and you can feel no back-of-the-mind guilt about shutting them out (which, as an introvert worrying about others' thoughts, _is_ an issue).
What you describe has nothing to do with being introverted.
To keep home and work separate. Maybe working from home for some is perceived as never leaving work.
That's a glass half-full/half-empty approach; conversely, I end up being more productive, working more minutes, taking less breaks to socialize/browse. One benefit I didn't recognize immediately is that I gained valuable time by being able to eat at my own pace, often while working, rather than worrying about a sustenance/obligations time management equation with my lunch break every day when I should be working.
I no longer wake up dreading going to work. I get to get up at a normal hour, feed the family every meal, and spend about an hour every morning reading. A more convenient workplace, for me, does not exist; people are different. Every day feels like hours have been added to my life.
Home can be the same - I have neighbors. I can hear them from time to time. Headphones, though, are a solution, but so is just general background music. Some times of day/night are much better than others, but I don't always get the luxury of doing stuff at those times. All this said, I like working at home.
On the other hand, a coffee shop is filled with near-constant hums of noise. Park, restaurant, etc are all the same. Since no one noise jumps out to grab my attention, I'm actually less distracted. No one cares I'm there for the most part (libraries aren't so good at this bit, but are better now that I'm older).
The other positive of working at a coffee shop is the change of environment often brings a sort of creativity. I find this especially so if I've walked a bit to get there, and even more so when I'm out of town or out of country. Granted, I'm generally working on artwork instead of "real work", so maybe this bit is just me.
I regularly work out of coffee shops, for hours and hours at a time even, and unless you absolutely dread even the slightest interactions, "Hey is someone sitting there?", other patrons generally leave you to your devices figurative and literal. If you do summon the courage to talk to people, you get a nice mix of regular baristas and patrons as well as a revolving door of new faces to meet and exercise your social and networking skills.
The tradeoff for a few bucks a day was worth it to me. I can't afford a co-working space and while that would probably be better for long-term professional networking, you can't deny the breadth of people walking into any given Starbucks.
Unlike others in this extended thread, I can't focus with people talking nearby or the music on the shop's speakers, so I put on the headphones with ambient music, classical, or white noise to keep out distractions.
Too quiet.
Bad internet. Gigabit, but they filter/firewall the heck out of it.
No coffee/snacks allowed
Bad hours. Some days they open at noon, some days they close at 6p, never open after 8p or before 10a
I understand this can vary significantly based on location, but this is what I have noticed in my city.