This is the thing. The sightlines and pillars are so big it's literally difficult to see other cars on the road with you.
That alone should warrant some safety regulation.
I knew things were off the rails when I parked my beater 2nd-gen Ranger next to a then-new F-250 and couldn't see the top of the Ranger's cab when looking through the F-250's windows.
I don't think main street has an argument any more for why we should risk getting run over for out of town shoppers and office space can largely be rezoned.
I don't particularly like the experience of walking in a city with bikers, but at least they are engaging in as much risk as they put others through and accidents with them are likely to be short term inconvenience instead of permanent injuries and death.
Because people of all capabilities need to get to the businesses in the cities. If you're proposing prohibiting private transportation, you first need adequate public transportation, which is expensive and often lacking.
The alternative, where _nobody_ has easy access to the city's businesses, tends to result in the businesses moving out of the city to somewhere else, taking their tax payments with them, often places that are _even harder_ to get to for people who don't have cars... because businesses need customers. If you won't support them (by providing affordable and convenient means for the customers to reach the businesses), they won't wait to die, they will solve the problem themselves.
Only cities which have well-developed public transport networks, and have very popular city centres (to the point of congestion) are even thinking of banning cars from them. The rest of the cities need all the help they can get to fend off financial ruin from e-commerce.
Popular cities don't really need to compete to fill a bunch of commercial real estate. They have people who commute every day by public transport and residents who are competing for real estate with this property.
It's enough now with the cars, there are mall towns and cities happily lose 'business' to them because it is not worth wasting 30% of all land to attract a bunch of people who may never actually get out of their car in your city and then at most to a business that probably pays less in property tax than a correspondingly sized residence.
These businesses can't vote and if they aren't in town to complain the noise from them stops. There were also a lot of angry horse cart drivers once.
But people in the US don't actually want that, unfortunately. They mostly like being able to drive around in cities (either their own city, or nearby cities where they want to visit). It's weird to say that, because most people would probably say they hate driving in city traffic. But when the alternative is driving to some sort of park-and-ride and switching to trains or buses, many US residents will prefer to drive.
Let's also not forget that even some of the most transit-heavy places in the world still allow private vehicles. In some (Tokyo especially comes to mind), it ends up usually being more expensive and take more time to drive than to take transit, but people still choose or need to do it for whatever reason.
Your phrasing of "why cities allow" is a common one, but remember that a city isn't its own entity with its own wants and desires. The laws reflect the wants and desires of the voters who live there.