The majority of women TTC between 35 and 40 will do so. A not insignificant minority, won't. "80%+" is, to be fair, decent odds but still means 1 in 5 couples face the heartache and uncertainty of infertility. That's not a remote risk - even though it's still more likely than not the dice will roll in your favour between 35 and 40.
Also relevant that time to conceive may be longer. Miscarriage risk is, sadly, higher. And (bearing all this in mind) if you'd plan to have more than one child, don't just think about your age when TTC the first child, look ahead to probable age when TTC the next.
If you do encounter problems, and seek fertility treatment, younger people statistically have better prospects of success in any given IVF cycle (if using own eggs, that is). The infertility may always have been an issue, that's true, but there is a better chance of a happy ending following treatment if you're younger when you embark on treatment.
Fertility MOTs can give false reassurance. A lot of infertility patients are "unexplained" and pass an MOT with flying colours.
The risks are just one factor in a very personal decision and everyone must weigh them in the balance for themselves, along with all the other factors relevant in their lives to the decision.
My personal decision was to wait (though I didn't fully understand the risks at the time). I landed up in the unlucky 20% and didn't conceive naturally, due to unexplained infertility. 3 years and some IVF later, I was lucky and got my miracle. I only have one child, though. I couldn't personally wish to go back and change anything, because I love DS to bits and if my fairy godmother could let me remake any of the decisions that led to DS, I wouldn't have him, I'd have a different child, and I wouldn't choose that. But I think it's important people have eyes open to the risks.