I bicycle commuted for years in an American city. It is as safe as your local council decides it should be, and my commute always felt safe. Don't give in to the belief that unsafe cycling is inevitable.
I would never bike commute where I live currently, and I don't think that will change any time soon despite it being a relatively left leaning urban area.
I biked for over a decade without incident for leisure.
Then I started bicycle commuting. Within one year I had not one but two occasions where I was knocked unconscious by angry rush hour drivers. I no longer could plan my destination but rather had to fight the entirety of traffic trying to get downtown at the same time at once. I still have trouble with one arm and the other time I believe I got a concussion after the driver destroyed my bike hitting me broadside and drove off.
I have about 3-4 years of biking as only transport including working as a full time professional bike messenger. I have never been hurt outside of rush hour. I have never been hurt on a planned leisure route. Only when I cannot pick the destination.
The hostility in my experience is like 10x dealing with angry to/from work rush-hour traffic headed to a dense job-rich area, especially with folks like soccer moms desperate to pick up their kiddy from daycare in time, etc.
As you note and in my experience the school drop off / pick up times are the scariest as you near schools and arteries on the school destination paths. There are frequently backups and gridlock situations at these times, coupled with palpable driver anxiety and hurriedness, which just seems like a recipe to get killed or maimed as a cyclist