This is a broad statement with no factual basis. We have 2 kids and I have been a stay at home mom since my oldest was born almost 13 years ago. My husband is a military officer. We have always lived in high COL areas (Southern CA and Northern VA). We are able to save for college, retirement, take vacations, etc.
I have a sister who lives in San Francisco. The actual city. She has 2 kids under 6. She stopped working 3 years ago. She has a part time job that she does mostly for fun, as she uses the drop in daycare there while she works, which almost negates her pay. Her husband is a creative director (graphic designer). They probably spend every penny they make, but they are not struggling.
I know several other people who have kids and only one parent works. It's not uncommon at all.
That said, we will have a military pension for life in about 2 years (husband will be 41). If my husband passes away before me, I will still get 50% of that pension, which will be around $8k per month by the time we are 70. So, me not working won't impact my future retirement much at all. We also have a separate retirement savings fund (TSP) and Roth IRAs.
My parents raised three kids on one income and are now retired in Florida at a retirement community. Their social security checks cover their living expenses and then some. They bought a brand new house when they retired and have about a $120k mortgage. Their payment is like $800/month. Their social security checks total around $4000/month combined. My dad has a small pension. They have a 401k with about $500k, ALL of which was saved in my dad's last 10 working years (he lost almost all of it during the recession in 2008). Right now, they are taking the minimum required distribution, but it is only coming out of the interest at this point. The principal hasn't been touched. So, it IS possible to save really late in the game and end up okay. But, my dad was a high wage earner at the end. He was able to sock away a ton of money at the end.