Well, there is an increased awareness of risk factors. Whether it is too increased or not can be debated – certainly Nancy Grace has given more than enough exposure to the mortal perils faced by attractive white girls/women every time they go out the door, vis a vis the actual risk.
I think we’ve also discovered or had a growing awareness of some truths it’s good to know. Pedophiles do exist, in some non-trivial proportion; they can’t be cured; they target children in specific patterns, a number of which involve/start with having access to talk to the kid in a context in which no adult is present. Some of this might not have been talked about in the past out of prudishness in discussing sexual issues, naivete (“Oh, you know Bob, he’s always been a bit off, but I’m sure that comment to little Timmy was just a joke, won’t happen again.”).
Some of it is increasing mobility (as in not living so much for years and years in the same small community, where you knew your neighbors, your neighbors could be proxy parents when they saw your kid doing something risky in your absence, where there were readily walkable/cyclable streets).
And some of it honestly is that parents back then were (consciously or not) more willing to expose or allow their child to be exposed to (low-probability) risks to life and limb. As we’ve learned about more risks, and come to an ever more offspring-centric middle class culture, parents now are less willing to tolerate risk. It doesn’t help that there’s a feedback loop. When you’ve taken ten protective measures against ten increasingly attenuated risks, when you’ve created a world in which few children get abducted or get concussions (or, compared to the past, die of whooping cough), it becomes increasingly rare for children to come to harm, thus breeding the illusion that risk of harm can and must be eliminated, thus incentivizing protective measure no. 11 against even-less-probable risk no. 11.
Also, shame. If your kid died in an accident 100 years ago, you had four others, it’s sad, but things happen, remember when Baby Alice died of typhoid and that Jenkins boy got shot to death out hunting? If your kid dies or gets hurt today, and there’s a measure you could have taken, a restriction you could have enforced, to prevent it – man, you’re the World’s Worst Parent On Earth.
To answer the OP more directly: yes, too overprotective, no, the objective risks haven’t changed as much as the protectiveness has, but yes, I can understand the impulse to coddle the kid if it were mine.