Exercisers generally want their barbell squats (or even their air squats and goblet squats) to get the butt as close to the floor as possible (ass to the grass). That is, lower than parallel (the photo shows a great example - that little gal is stronger than I am or will ever be but, in a half-hearted defense, shorter people have an easier time with squats because the range of motion is shorter. Same goes for bench press with smaller people - shorter levers).
Everybody needs squats unless there is a medical problem.
I am working on lowering by using gradually-lower box squats and lightening the weights. It is always too easy for me to find my sticking point after a few reps and then I lighten the weight.
Why bother going below parallel? Because it's another tough challenge to take on, and because it stresses all of the muscles involved in squatting even further. Stresses willpower too and we all need to strengthen that. That article doesn't even cover all of the accessory muscles involved in balance and core stability. Total body stress including your heart which pounds like it is at the edge but what doesn't kill ya makes you stronger, I hope...and you could do worse than croak on the gym floor.
I am thinking that I ought to do lighter-weight deep squats once a week, and my usual almost-parallel squats once a week. I have weak quads even after 2 years of this, relatively-speaking. I know we have a few powerful squatters at Maggie's, though.
Keep those knees out!