Because there is absolutely no reason for Manhattan to have Canals. And there were Canals, hence Canal Street.
The Canal Street canal was built to drain a swamp, not as a public thoroughfare. Although that could potentially be a POD - the swamp is drained earlier, and a few more connecting canals get built so the ships' boats can bring cargo directly to the warehouses.
If you want something more exstensive.
I don't think there are many American cities that are that mainly built on reclaimed lands and the ones that are old enough to be Venice-analoges are on somewhat hilly coastal areas. You have to remember that Manhattan is much, much flatter than it used to be for instance, having been heavily graded down.
Granted - I'd forgotten about that. But on the other hand, part of lower Manhattan
is built on reclaimed land (the shoreline is considerably farther out now than it was at the time of settlement) and the reclamation started in the 17th century. Compare 1660 and 1766 on
this map.
It actually seems, from the same map, that Peter Stuyvesant did dig a couple of canals, along what are now Broad Street and what looks like Beaver Street. So the trick is to keep and expand them as more land is reclaimed, rather than filling them in. Would it be enough if the Dutch kept New Amsterdam a couple of generations longer?
Rio de Janeiro also has a lot of reclaimed land, and was founded in 1565. Maybe the Dutch could win out against the Portuguese in their struggle for Brazil, or a Portuguese governor could get the idea from them.
The other major cities on the east cost are likewise hilly because they are mostly on the fall lines of rivers.
Boston's pretty flat, and the Charles, like the Hudson, is an estuary for the last few miles of its course. And Back Bay is built on reclaimed tidal flats, although they weren't filled in until the 19th century.
One way this seems doable is to have the railroad delayed enough somehow that canals are actually useful when some of the Great Lakes port cities develop. Another way to apply this to DC, incidentally, would be to find a way to keep the Washington City Canal from becoming stagnant and an open sewer, maybe by linking it to the C&0 Canal or by diverting the mouth of Rock Creek into it. This would probably require Washington to remain a fairly substantial port and the PoD mentioned above of delaying the spread of the railway somehow.
Hmmm. Some of the Great Lakes cities - Buffalo, for instance - were starting to develop before the railroad came in. There's about a 20-year window between the opening of the Erie Canal and the first through railroad to Albany. Maybe the Erie Canal project could include some city canals?
The topography is right, but it would require earlier local industry so that Buffalo would be more than a transit point.
New Orleans might also be a good candidate for this treatment-old enough to fit the kind of image the OP seems to be looking for and low-lying enough for canals to be viable. But with that city it'd be especially difficult to minimize health hazards so they don't get filled in at first opportunity.
NOLA is
too low-lying, maybe - it would be hard to flush the canals, and they'd get stagnant. Amsterdam is a meter or two above sea level, and even there, some of the canals became unhealthy during the 18th century. I'm not an engineer, but I'd suspect that a city actually below sea level would increase the problem significantly.
EDIT: How could I forget Mexico City? There were extensive canal systems at Tenochtitlan and Xochimilco, and although Mexico City is at a high elevation, the terrain is flat and the central city is mostly landfill. The trouble is that Mexico City isn't a seaport, so there'd be no reason to keep or expand the canal system (except for recreation, as Xochimilco is used today).