That’s a common misconception. My wife specializes in OB/GYN as well. It doesn’t really get unsafe, the risk factors just go up. At no point do they actually become unfavorable. Trisomy 21 is a perfect example. Worst case scenario is 1 in 25 chance of having a child with trisomy 21. Any gambler will tell you that 25:1 is as close to a sure thing as you’ll get. The risk is there, but the odds are heavily in favor of a healthy baby.
It’s all in the parsing of the numbers. Explained as I did above, it doesn’t sound bad. 25:1, not bad odds. Or you could send an expectant mother of advanced maternal age into a panic by telling her that her chances of having a trisomy 21 child are 56 times higher than they were at 21. Which is also true.