I think you're biased towards where you live. Where I live, cycling is definitely not considered risky, there are plenty of bike paths, and many people do indeed let their children bicycle as their primary means of transportation. One of the benefits is that the children can get around on their own and be more independent.
And yes, 30 years ago there were far fewer bike paths here. So things can change.
something like 70% of total distance traveled is by car (https://www.statista.com/statistics/449436/netherlands-modal...) and yet there are fewer annual motorist fatalities than bicycle fatalities (207 cyclist fatalities versus 175 motorist fatalities in 2021: https://www.statista.com/statistics/523310/netherlands-numbe...).
EDIT: cycling in the netherlands is about 685% more dangerous than driving per https://www.cbs.nl/en-gb/news/2020/31/decline-in-road-fatali.... Of course, this isn’t a like-for-like comparison since the distance traveled by car skews more toward the more dangerous highway miles while cycling skews heavily toward the much safer local/city streets—if you account for that, the difference becomes even more pronounced.
This very much feels like "in addition to" rather than replacing a car, at least in the US. My wife and I (without kids) tried living without a car in one of the largest, most walkable cities in the US and it was doable, but it's just soooo much nicer to have a car. Coordinating rentals or even ride shares are a lot more tedious than jumping in a car and driving, and even if ride shares are cheaper than car ownership, I would often find myself not doing things because of the cost of ride share / car rental / etc. Further, I would have occasional ride share drivers blow me off when I really needed to be punctual, and I also had some fraudulent experiences with car share companies (upcharging me for services that I've explicitly declined and not correcting it via customer support channels).
There's also public transit, but that takes wayyyy longer to get around and it's also really dirty, crime-y, and otherwise uncomfortable at least in the cities I've traveled around in.
Lastly, cycling is probably always going to be less safe than getting around by car (we can and should improve cycling safety, but I don't know that we're ever going to get to parity with driving) and I don't know that very many people are going to want to subject their kids to that risk as their primary form of transit. I probably wouldn't, realistically.