When I started squatting, my knees were so weak I couldn't walk up a flight of stairs without pain. I finally started exercising because my doctor gave me a look of disdain, handed me a sheet of basic exercises and told me to get out (edit: when I went to her to ask about my knee pain...)
I'm not going to argue for (or against) working in squatting position, but squats done properly are not going to hurt your knees.
Is that a specific type of squat, or just a normal squatting position without any weight?
A crucial difference from how many westerners squat is that the weight is carried back on the heels. Westerners tend to squat with weight forward on the toes, which is highly fatiguing.
There's a vintage video on the topic:
https://www.youtube.com/watch?v=y76UbfBr5vo
(This was linked in the article, but it's since gone walkabout).
When people unused to squatting squat down, they often end up barely reaching parallel.
In contrast to the western "catcher's squat" (from baseball) where the heels are off the ground and the weight is on the balls of your feet.
In China, until recently, all toilets were basically squatting toilets, yet octogenarians had no issue squatting to use them... how old are you that you can't do for 5 minutes what an 80 year old can do several times a day?
Also, I'd like to point out the differences in length of time between taking a shit and a normal 8 hour work day.
I'm not saying this is impossible, but I understand the trepidation.
And we still don't have any arguments supporting either position. I do squat for a few minutes every day to facilitate my squat lifting workout but don't see an inherent benefit. I suppose one can argue that it has been a natural movement for so long that our bodies may be genetically designed for it.
My mobility is still poor compared to what it was when I was a child, but at 38 I'm now finally more flexible again than I was at 25, maybe more so than at 20, and it's great to not feel constrained by weird movement patterns.
long-limbed people have more difficulty with this, while shorter-limbed people don't have difficulty with this after a little stretching