Our open office shows that it's not about space. There's still a lot of space between desks, enough to have cubicles. There are several empty seats even. The rest of the office has tons of barely-used employee space, like big table tennis rooms and open seating. The desks are always arranged in a way that the screens are facing everyone walking by.

To put it another way, I can just take my laptop and work in a common area with a wall behind me, and I get more space and privacy. That's what I do.