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You start to lose perspective that most people aren't in either group.

At a certain point, which America passed long ago (which I write as a dual citizen), there is not more a question of "perspective." The Right burned that to the ground. Started before Nixon was elected, gained full stream under Gingriche's Contract On America, and was here to stay with Bush the Lesser paving the way for Trump and the Qanon and Christofascists.
The perspective you seek is a myth propagated by people who look to some - very long past - degree of dialog. I'm sorry my friend, that dialog doesn't exist any longer in any meaningful way. Your complaint that everyone is lost in their own media/existence bubble, while in some way is correct, is a false equivalency. Sometimes one side is right, and another is wrong and has been historically so for decades.
So, back to the question of third places, one needs only look abroad to Europe and even most of the other anglophone countries to find them, and see their merit. It's not just tony coffee shops. And it's not just the developed countries. The third place is essential in many developing economies. It's the football pitch where your son is playing with another man's son who just happens to live in "the ghetto." It's that "ethnic" (written in scare quotes because who knows where you are) restaurant that you frequent and get to learn the ways of the owners and workers because you love the food.
The USA used to have this decades ago. It still exists on smaller scale in middle America. But by and large the propaganda of the right has killed any desire of the average middle American to engage in any meaningful way with those outside their own "kind." 
i.e. the middle place had no place in America anymore. That doesn't mean it doesn't exist outside America.
I wouldn't say I liked where we lived when we first moved to Omaha in 1989. It was half a mile from our house to anything. Heck, the nearest grocery store was 2 miles away. 
But it was a "nice, quiet neighborhood" with "good schools".
By the late 90s, the office park across the 'stroad' finally got some in-fill with restaurants and a couple of stores. We still lived a quarter mile from the stroad.
I went to college in nearby Lincoln. When I moved off-campus I lived in what some derisively called "South Central" or "Alphabet town". But I loved how walkable it was. There was a fantastic bakery, a small grocery store, and a couple of locally-owned restaurants within 3 blocks of my apartment. 
I want to live in such a neighborhood again, but this time without the crack houses and ever-present streetwalkers. You stayed on the Runza side of south 13th... >

I truly think part of my political journey was more influenced by NotJustBikes than other properly political content creators. >

friendly edit: NotJustBikes
edit: Only noticed because I'm subscribed. Fascinating content. >

Done. Thank you. >

Absolutely it does, check out Jane Jacobs' Death and Life of American Cities, she has some awesome points that may interest you. >

Been meaning to read that one, worth it? >

Easily one of the best books I’ve read and I say that as someone who has very little background in urban planning. Her writing is amazing and reading her ideas is cathartic for anyone who lives in a major city. >

It's an interesting question, and one worth considering - but I think the answer is no. 
First, I want to discuss why I don't think our city planning is materially responsible for polarization, and then, second, I'll go into what I think actually causes it. 
I've lived in all three types of generalized environments - urban, suburban, and rural. I grew up with blue collar parents, and am now a white collar attorney. I've run the gamut, and I've experienced a lot of different ways of living in the US. 
When I lived in a major city, I didn't have a car and did all my travel via foot, bus, and subway. Based on this experience, my take is that personal cars and sprawling suburbs are not nearly as isolating as people make them out to be. As much as people like to romanticize the community aspect of city life, when you actually live in it, day to day, you end up just trying to get through that community to wherever you're going. There are people all around you - crowding the sidewalk, packing the subway car like sardines, and ahead of you in every line. You're surrounded by community and other people, but they all just become NPCs that you try your best to avoid. You don't try to strike up conversation with random members of the community on the bus.
And I think the same is true for the supposedly isolating nature of single family homes. I never got the sense that I knew my neighbors any better when I lived in the city than I do now. In fact, I'd argue that I've known my neighbors in the suburbs far better than anybody in any apartment complex I've ever lived in. In a suburban single family home, I know that my neighbors are going to be there for a while - I can rely on building those relationships. Meanwhile, the guy in the apartment next door is probably going to move somewhere else in the next 18 months. While I might only talk to my neighbor once every other week, there were stretches for years where I never spoke to a single soul in my apartment complex. It always completely felt pointless to get to know anybody in the building. 
Now that I live in the suburbs, I don't feel like my connection to the community is really any different at all. I talk to exactly the same amount of people in my car now as I did when my commute was via subway - exactly zero. My 30-minute commute via car isn't any different than my 30-minute commute via walking and subway. Seeing political bumper stickers or panhandlers at a traffic light is exactly the same as when I'd try not to make eye contact with people handing out flyers or begging for change. The difference with the commute via car is that it's far more pleasant, at the expense of being occupied while driving instead of being able to read - but there's simply no functional difference in terms of community involvement. 
There is a lack of a physical "third place" in modern society, I'll agree with that - but I'd argue that, this two, has nothing to do with city planning, and is lacking just as much in urban areas as it is in the suburbs. A 15 minute bus ride to the bar in the city isn't any different than a 15-minute drive to the local suburban bar. The truth is simply that people are going to these places less regardless of where they're located. 
And this is tied in with my second point - what I think is actually causing the problem with polarization and lack of community.
The rise of in-home media, social media, and the internet in general has made the physical "third place" a hard sell. Why go to the movie theater when you could stream it at home? Why go the mall when you can browse Amazon from your couch? Why go to a friend's house to play games when you can all do it digitally from your computer? 
It's not that the private car has made you pass these things by - you did and do pass them by while you push through the crowd to get on the subway, too. It's simply that it's hard to motivate yourself to go out to a "third place" when the internet has become the ultimate "third place." 
Now mix in social media algorithms designed to get clicks through rage and you have a perfect storm. People are staying home to participate in the new digital "third place," and in the process aren't ever seeing a real cross-section of the world anymore. All they see is the carefully curated internet environment that they've subconsciously (or consciously) shaped for themselves by blocking everything they don't want to see, except for the very most extreme things that piss them off and that the algorithm knows will make them click. 
You never meet Bob, the generic moderate Republican who actually agrees with you about universal healthcare anymore. On the internet, you've blocked Bob and any media that presents as aligning with him. For all intents and purposes, he doesn't exist for you. But you absolutely hear about Karen the shrieking Qultist, because no matter how much you want to or try to block that, the algorithm knows that you'll immediately click on it. Meanwhile, you've curated your "friendly" feed in the opposite direction. You never meet Debbie, the generic moderate Democrat who doesn't agree with your progressive politics. She doesn't exist for you. But your feed is full of Bernie and a mishmash of Twitter personalities parroting exactly what you want to hear - specifically because you invariably like those tweets and click those links. 
So you end up with a "third place" where only two groups exist: those who agree with you completely, and those who  agree with you on nothing. You start to lose perspective that most people aren't in either group.
Edit: I don't think I'll be replying to anything else in this thread. I made a good faith effort to discuss this as calmly and as neutrally as I could, but I'm getting a number of aggressive, confrontational responses that are more interested in expressing their hatred than discussing the actual question in the OP. At least the OP seems to be extremely relevant.