I think a bakfiets should work well for carrying very small kids. I see a fair number of them in my neighborhood.

Making brake levers small enough must be hard. Once they make the levers small (small distance between lever and bar) then it may not be able to pull enough cable. They have improved, though, with clever curve designs. You may find that upright bars are better, because the lever problem there is solved. If you like bending over, get a low stem or use North Road bars upside down.

Driving your kids in cars is dangerous. It might be more dangerous than carrying them on a bike. This is counterintuitive, and since people don't use bikes much in North America, they tend to assume the bike is more dangerous. It's just ignorance.

But I do agree that letting them ride in NYC streets alone is not right. Not until they're around 13. When they're 9 or so, they can ride in the street with you, preferable with you in back so you can watch them and offer corrections. You can also "cover" for them.