I'd bet that much of the issue stems from the decline in birth rates among middle/upper middle class parents relative to the days of yore. When you only manage to pop out one or two kids, at great career sacrifice and monetary expense, each one seems to matter more than they did back in the day.
Also, paradoxically, the safer things get the more people worry about the dangers that remain. This is rational. Say doing this or that during pregnancy results in 1 in 10,000 women dying during child birth. If 1 in 100 women die during child birth anyway, it's not a big deal. But if improvements in medical technology gets the base rate down to 1 in 10,000, then suddenly you're talking about doubling your risk.
I would say it's got less to do with the perceived (even subconsciously) value of the children, and more the experience of the parents. For the first child, you're often hyper-conscious of threats and problems. With later children you've better assessed what's important to pay attention to and what isn't.
Anecdotally speaking, this is not true. My parents always joke that I was the "test subject" for their parenting experiments, and my (younger) sister is the one on whom they actually applied what they learned. Growing up, my life was pretty care-free. My sister on the other hand is definitely suffering from "helicopter parenting."
Gender probably has a lot to do with it. I'm a guy, so I don't have as much to worry about (whereas girls are perceived as more vulnerable to things like rape, etc.).
I can confirm this was a big issue with our children. Our first we tended to treat like porcelain... eventually we've learned through experience that kids are more resilient than you may otherwise think.
I became a parent later in life, and I do think that is a factor. In addition to how hard it is to have a kid, I personally have a much greater sense of my own mortality now then I did in the early 20s. It's hard not to let this color the way I parent.
"First kid - food drops on the clean floor - burn the food sterilize the place. Second kid - food drops on the clean floor - wash it and give it back to him. Third kid - she ate the cat's dinner? It's the cat's problem, not mine."
Also, paradoxically, the safer things get the more people worry about the dangers that remain. This is rational. Say doing this or that during pregnancy results in 1 in 10,000 women dying during child birth. If 1 in 100 women die during child birth anyway, it's not a big deal. But if improvements in medical technology gets the base rate down to 1 in 10,000, then suddenly you're talking about doubling your risk.