The biggest delivery truck traffic is for furniture, goods (one or two UPS trucks for an entire building), or garbage. No amount of drone tech can reduce/eliminate truck traffic for an entire building.
The slightly more sane idea would be to look in the other direction, and build underground. That would be extremely expensive and have to deal with all sorts of issues, but at least it's physically possible.
The actually realistic solution is to focus on developing housing and infrastructure in the outer boroughs; Brooklyn and Queens are full of the absolute worst kind of inefficient quasi-suburban accumulated sprawl.