I'm interested in how specific this PhD experience is to the US, certain subjects or recent times. My own experience doing a maths PhD in the UK in the mid-2000s was not like this at all (but had a different set of challenges for sure).
Yes, my advisor emphasizes papers a lot, but there aren't any requirements for number of papers for graduation. While there are extremely busy periods of forgoing sleep to work (eg right before a major deadline), my advisor also constantly reminds us to take breaks and enjoy life. There was also the anxiety about graduating on time, but that too was sorted out by just having a meeting with my advisor and understanding how things work.
On the other hand, the situation with the qualifying exam was the opposite, I had to constantly remind my advisor that I needed to get that done. It involved a 50 page report on the current status of my research and a thesis defense style presentation to my committee, so that was a bit of a challenge to make time for between normal research. Passing it didn't feel like much of a challenge, just meeting the 50 page requirement did. I had enough data, but it was still a lot of writing.