cover it up

assuming the pioneers were not covering bridges for aesthetic reasons or to deliberately be charming so that future generations would
take photos and post them on blogs,

why build and maintain a cover for a bridge?

answer from coverbridges.com:

Early attempts at wooden bridge building were at the expense of an  uncovered bridge called a plank bridge. With no means to treat the wood such as pressure treated creosote as we have today, they quickly rotted and fell in. Soon they figured that they needed to cover them.

A secondary benefit of covering the bridges also aided the horses, some horses are leery of crossing a bridge especially when they can see or hear the running water beneath. By placing the floor boards close together and painting the bridge red (If one looks closely at a Parke County covered bridge. It looks much like a long barn would). It helped the horse go right through the bridge with no problems.

Another secondary benefit of a bridge being covered was for the gentlemen. During horse-and-buggy days, it was proper to court your lady in your carriage. What better place to do this outside of the watchful eyes of the public than inside a covered bridge? This gained them the title of "Kissing Bridges" for a short time.