The volume gets pretty intimidating; for Manhattan, you're talking around 140 cubic yards of garbage per block per week [0.1 yard / person, 1400 people / block], which would be ~4 of the 40-yard dumpsters (the 8 x 8 x 22' ones you'll see outside construction sites, roll-on/off trucks) per block.
That they're able to collect that much garbage anyway means it's not an unsolvable problem, but going from using that much space once a week, in the form of piles of garbage on garbage day [with the remainder of the time it being scattered in smaller piles in buildings' garbage rooms], to 24/7, means you're losing like 12 parking spots per block, or like half a building lot per block, if you're storing them off the street.
By your calculation, they would get 12 parking spots worth of random small pockets of space back per block. In reality, it would be more than that in usable space, because who want to do anything directly next to a distributed pile of garbage?
That they're able to collect that much garbage anyway means it's not an unsolvable problem, but going from using that much space once a week, in the form of piles of garbage on garbage day [with the remainder of the time it being scattered in smaller piles in buildings' garbage rooms], to 24/7, means you're losing like 12 parking spots per block, or like half a building lot per block, if you're storing them off the street.