You're right, but this is very difficult for an employer to implement for people already on the job. Law enforcement agencies have had this problem for years. Most have a physical fitness standard for hiring and during training, but nothing after that. This is how you get all those fat cops you see. Departments that have tried to put physical fitness standards for in-service folks into place have been countered with expensive lawsuits that the employees often win. Moreover, when these out-of-shape employees begin to exercise at the behest of their employer, they tend to get injuries from doing that.

My old department had an annual physical fitness test that everyone had to take, but that no one had to pass (no, I'm not sure what the point of it was, either). One of the tests was a sit-and-reach flexibility test. Every year, the same officer would take the test and then put himself in for an on-the-job injury to his back from overstrain. He would be off work for at least a month, and I have no idea what medical costs ensued.

Where the TSA is concerned, their OTJ injuries come from the same sort of activities that warehousemen and stock handlers perform - lifting and carrying things. Proper techniques, wearing back braces/lifting belts, and asking for assistance when something is too heavy can all prevent injuries, and safety awards promote this. It's a practice widely used in private industry, and tends to reduce injuries. If it didn't have a positive effect on the bottom line, private industry wouldn't do it.