...that the Parshendi could have easily attacked the mobile bridges at any time and stranded the Alethi armies. It was noted that they jumped over armies to attack from the rear. It wouldn't take much for a small force to jump over them and slaughter the defenseless bridgemen.

The only time they really attacked the bridgemen is while they were laying the bridges for the Alethi armies to cross. Once the bridges were down, they mostly focused on the soldiers.

That's not to say that they wouldn't burn the bridges down once the armies had retreated, which goes back to what I said about the cost of permanent bridges vs. mobile ones. But as a combat tactic? I don't think it fits.