Sure, obviously things could be improved, but come on, it's not like it's hard to get around Manhattan without a car. This isn't a suburb of LA, it's a region with dozens of heavy rail transit lines running 24/7. If Manhattan can't support every other street being car free, literally nowhere else on the planet can.

... We're saying that Manhattan, specifically, needs more transit options? It's the most transit-accessible region on the continent, I don't know what more you could want if Manhattan is insufficient for you.

If the lanes were re-opened, traffic would immediately improve along the route. People would notice the lack of traffic, and start driving more, since now it's convenient. The number of cars driving would increase until traffic was so unbearable that people are encouraged to use other methods of getting around, changing when they make their trip, or just don't make the trip at all. If the bottleneck isn't in this section of road, it'll be somewhere else along the route, but somewhere is going to be completely choked in traffic. This plays out over and over again with every freeway widening project, I don't see why we'd expect this to be different.

I don't know what your definition of "downtown Brooklyn" is, but when I look on Google Maps, the BQE next to the Manhattan Bridge is literally a block away from the "Downtown Brooklyn" bridge, and it basically divides Dumbo from the rest of Brooklyn. I'm struggling to imagine what you think would qualify as going through downtown Brooklyn, if you don't think this counts.

The BQE doesn't circle the city, it goes right through the heart of downtown Brooklyn.

Cities don't need highways to function, there's plenty without them in Europe and Asia. Even in North America, Vancouver does just fine without a highway.