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I think this is my favorite explanation. There was no essential need for a bridge but building one would have certainly made for a grand entrance and indeed elevated perspective to the newly demarcated estate plots. As Edmund points out above the bridge doesnt go over the river but I acknowledge that that it could have added a challenge to cross although Sheffield was well in to culverting season by this point. So on that basis of what Rover says I would see the bridge as a means by which the new residents of this area could literally elevate themselves above the other existing residents by making such conspicuous and no doubt grandiose entrances and exits to the estate. It must have added to the desirability of the place.