The discussions in the office however are sometimes related to what I'm working on. So hearing bits and pieces of them stands out in my mind and can get me thinking about that instead. People in cafes are also very unlikely to come up and tap me on the shoulder and start asking questions about completely unrelated topics.
YMMV of course and some people concentrate just fine in loud places. On the other hand the people that say "I don't mind the open office plan, it doesn't bother me" might just be the people who are disrupting everyone else.
In an open-plan office, the people around you are usually your coworkers, the people you see every day and know personally. In a coffee shop, they're usually total strangers, people you might see occasionally at that shop at best, and very likely you'll never see them again.
Also, the strangers at the coffee shop don't care what you're looking at on your laptop, or if you're getting any work done. Coworkers might. Also, strangers at a coffee shop are unlikely to interrupt you; coworkers are very likely to. So at the coffee shop, it's entirely possible to be around other humans without being forced to socialize with them, but not at work.
This is much different than the office environment.
Imagine: Someone's else half-duplex conversation with their significant other about what colors to paint the bathroom this weekend or how much fun a guy had at the bar with the girls from the other division or the hen-pecked husband accepting orders for what to bring home from the Pret-a-manger don't even come close. Then there are the custom ring tones and chatter from random cell phones, the rustling of strangers between the cubicles as new employees are given the tour. A random maintenance person wanders around holding a ceiling tile and pack of fluorescent bulbs knocking the step ladder about having another half-duplex conversation about last night's sporting event.
Your kid's "play" don't even come close to this, because you're not working in the traditional office environment, you're working at home.
As a result I had to get a desk in a co-working space. Not cheap but I find grown ups bantering loudly far less distracting than my kids asking me to play.
My team used to be clustered into a corner of the building. Pairs worked quietly, louder teams weren't around to bother us, etc. It wasn't quite as nice as actual offices, but it was pretty close.
A full-on open plan office sounds terrible. Working most days with kiddos playing sounds terrible (when I work from home, I get most of my work done during his nap and after his bedtime). Working in cubes near noisy teams isn't great. Working in cubes secluded from noisy teams is fairly nice. I think I'd like to work in a team office to allow easy collaboration, while keeping away distractions.
I know of a couple coworkers that do not have trouble concentrating in our open office, while I continually struggle to get deep thought done.