I read the article and I can empathise - I think it's more common than people think.
Perhaps regret is too strong a word. I love my 2 DC and they mean everything to me, but I do find it so hard juggling it all, at the cost of my personal identity - even with a supportive DH. I think these days with nuclear families, urban lifestyles (having to work and live in or near cities) childcare and general living costs, high parental expectations... being a mum is tough. I say mum because mums have had to evolve their historical role in families over the past centuries. Today in modern developed societies, girls are educated and start in work just like men, we get to travel, gain confidence in our vocation .... then we become mums and struggle with everything - guilt if you took time for yourself, guilt if you pursue work/business etc, guilt if you didnt organise the household, failure if your kids didnt conform to "normal" or national education standards etc. If you have easy going normal healthy kids, great. If you have money challenges, disabilities or learning difficulties, an unsupportive partner/family.. it's a relentless and thankless job can really drive you to the edge.
With my DD in particular I always wonder what I'd tell her... unlike me, she's naturally maternal and caring, but she's also bright and talented and could do achieve much more without kids. I'd love to pass on my thoughts but I cant, because it would send the totally wrong message that I regret having kids.
Btw I'm pretty sure my MIL and mother feel the same way because they never pitch in to give us a break, ever.