The "city on a bridge" that I'm envisioning has the entire population living their entire lives on a habitable bridge or a series of such bridges over major rivers, only going on land for recreation or for work-related reasons (farming, hunting, logging, mining, etc.). All housing and businesses that don't need to be on land would be on the bridges. Travel within the city would mostly be by foot, bike, or public transit (light rail along the bridge, ferries between bridges).
My thought process here is, once a civilization has the resources and know-how to do so, they could build a bridge above the heights their rivers are known to rise to and limit how much land they're taking up to what they need for farming. And even then, a lot of their farmland could be replaced once they are advanced enough to use hydroponics, aeroponics, and the like to grow a lot of their food on the bridges. That leaves more land for old growth forests, wildlife, and ecosystems writ large to flourish.
The main concerns I can think of would be how the foundation of the bridges would affect the riverine ecosystems, how the bridges might change the downstream flow of rivers (which could easily affect many other aspects of the larger ecosystem in the area), and how the handling of waste products might more directly pollute the water.
There are probably many other factors that I've failed to consider, but I'd like to know what the main concerns would be and how this sort of city would measure up, sustainably speaking, to a more typical land-based city. For the sake of argument, assume that the people in this city behave similarly to current eco-conscious populations (e.g. in Scandinavian countries) and, if I may ask, please compare the results to those current land-based populations. If you wish to expand the scope, I'd greatly appreciate thoughts as to the differences for more and/or less eco-conscious populations, too.
To clarify: my question is whether two otherwise similar peoples, one living on bridges (not needing to clear out land for themselves) and the other living on land, would have any significant difference in their footprint. I fully understand that many other factors probably play much larger roles in a society's footprint, but I'm concerned with comparing a bridge-based city with a similar land-based city.